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                                                                   Exhibit 10.12

                                 WARRANT NO. 1

THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE BEEN ACQUIRED FOR INVESTMENT
AND HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR
ANY STATE SECURITIES LAWS. SUCH SECURITIES MAY NOT BE SOLD OR TRANSFERRED IN THE
ABSENCE OF SUCH REGISTRATION OR AN EXEMPTION THEREFROM UNDER SAID ACT AND ANY
APPLICABLE STATE SECURITIES LAWS.

                              WARRANT TO PURCHASE
                         STOCK OF GENOMICA CORPORATION

          This certifies that FALCON TECHNOLOGY PARTNERS, L.P., or its assigns
(the "Holder"), for value received, is entitled to purchase from GENOMICA
CORPORATION, a Delaware corporation (the "Company"), the Maximum Number, as
hereinafter defined, (i) if a Qualified Financing (as such term is defined in
that Convertible Promissory Note (the "Note"), of even date herewith, between
the Company and Holder) is completed on or before May 31, 1997, of fully paid
and nonassessable shares of the Company's New Preferred Stock (as such term is
defined in the Note) for cash at the original issue price per share of the New
Preferred Stock issued in such Qualified Financing; or (ii) if a Qualified
Financing shall not have occurred prior to the date of exercise (and such
exercise occurs prior to May 31, 1997) or if a Qualified Financing shall not
have occurred on or before May 31, 1997, at all times thereafter, of fully paid
and nonassessable shares of the Company's Series A Convertible Preferred Stock,
par value $.001 per share (the "Series A Preferred"), for cash at the
liquidation preference (currently, $.6024) of the Series A Preferred then in
effect at the time of exercise (in either case, the "Stock Purchase Price").

          Such purchase may occur at any time or from time to time during the
Exercise Period, as hereinafter defined, upon surrender to the Company at its
principal office (or at such other location as the Company may advise the Holder
in writing) of this Warrant properly endorsed with the Form of Subscription,
attached as Exhibit A hereto, duly filled in and signed and upon payment in cash
or by check of the aggregate Stock Purchase Price for the number of shares for
which this Warrant is being exercised determined in accordance with the
provisions hereof.  The "Exercise Period" shall commence on the date hereof (the
"Commencement Date"); and shall extend up to and including 5:00 p.m. (Eastern
time) on the earlier of (X) the closing of the initial public offering of the
Company's Common Stock pursuant to a registration statement (other than on Form
S-4 or S-8 or a successor form thereto) under the Securities Act of 1933, as
amended (an "Initial Public Offering") or (Y) November 30, 2001, such earlier
day being referred to herein as the "Expiration Date".

          "Maximum Number" shall mean that number computed using the following
formula:

                                       1.
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                    M = (.15)x(P)
                        ---------

              S

          Where M =  Maximum Number

                     P =    the principal amount disbursed by the Holder
                            pursuant to the Note

                     S =    the Stock Purchase Price.

          The Stock Purchase Price and the number of shares purchasable
hereunder are subject to adjustment as provided in Section 3 of this Warrant.

          This Warrant is subject to the following terms and conditions:

            Exercise; Issuance of Certificates; Payment for Shares.
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               General.  This Warrant is exercisable at the option of the
               -------
Holder of record hereof, at any time or from time to time, commencing on the
Commencement Date up to the Expiration Date for all or any part of the shares
(but not for a fraction of a share) of New Preferred Stock, Series A Preferred
or any other security which may be purchased hereunder (hereinafter referred to
as "Stock"). The Company agrees that the shares of Stock purchased under this
Warrant shall be and are deemed to be issued to the Holder hereof as the record
owner of such shares as of the close of business on the date on which this
Warrant shall have been surrendered, properly endorsed, the completed, executed
Form of Subscription delivered and payment made for such shares. Certificates
for the shares of Stock so purchased, together with any other securities or
property to which the Holder hereof is entitled upon such exercise, shall be
delivered to the Holder hereof by the Company at the Company's expense within a
reasonable time after the rights represented by this Warrant have been so
exercised. In case of a purchase of less than all the shares which may be
purchased under this Warrant, the Company shall cancel this Warrant and execute
and deliver a new Warrant or Warrants of like tenor for the balance of the
shares purchasable under the Warrant surrendered upon such purchase to the
Holder hereof within a reasonable time. Each stock certificate so delivered
shall be in such denominations of Stock as may be reasonably requested by the
Holder hereof and shall be registered in the name of such Holder.

               Net Issue Exercise.  Notwithstanding any provisions herein to the
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contrary, if the fair market value of one share of the Company's Stock is
greater than the Stock Purchase Price (at the date of calculation as set forth
below), in lieu of exercising this Warrant for cash, the Holder may elect to
receive shares equal to the value (as determined below) of this Warrant (or the
portion thereof being canceled) by surrender of this Warrant at the principal
office of the Company together with the properly endorsed Form of Subscription
and notice of such election in which event the Company shall issue to the Holder
a number of shares of Stock computed using the following formula:

               X = Y(A-B)

                                       2.
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            A

          Where X =  the number of shares of Stock to be issued to the Holder

                     Y =  the number of shares of Stock purchasable under the
                          Warrant or, if only a portion of the Warrant is being
                          exercised, the portion of the Warrant being canceled
                          (at the date of such calculation)

                     A =  the fair market value of one share of Stock (at the
                          date of such calculation)

                     B =  Stock Purchase Price (as adjusted to the date of such
                          calculation)

For purposes of this Warrant, fair market value of one share of Stock shall be
determined by the Company's Board of Directors in good faith; provided, however,
that in the event the Company makes an Initial Public Offering, the fair market
value per share of Stock shall be the per share offering price to the public of
the Company's Initial Public Offering.

               Shares to be Fully Paid; Reservation of Shares.  The Company
               ----------------------------------------------
covenants and agrees that all shares of Stock which may be issued upon the
exercise of the rights represented by this Warrant will, upon issuance, be duly
authorized, validly issued, fully paid and nonassessable and free from all
preemptive rights of any shareholder and free of all taxes, liens and charges
with respect to the issue thereof. The Company further covenants and agrees that
during the period within which the rights represented by this Warrant may be
exercised, the Company will at all times have authorized and reserved, for the
purpose of issue or transfer upon exercise of the subscription rights evidenced
by this Warrant, a sufficient number of shares of authorized but unissued Stock,
or other securities and property, when and as required to provide for the
exercise of the rights represented by this Warrant. The Company will take all
such action as may be necessary to assure that such shares of Stock may be
issued as provided herein without violation of any applicable law or regulation,
or of any requirements of any domestic securities exchange upon which the Stock
may be listed; provided, however, that the Company shall not be required to
effect a registration under Federal or State securities laws with respect to
such exercise, except as provided by other agreements between the Company and
Holder. The Company will not take any action which would result in any
adjustment of the Stock Purchase Price (as defined in Section 3 hereof) if the
total number of shares of Stock issuable after such action upon exercise of all
outstanding warrants, together with all shares of Stock then issuable upon
exercise of all options and upon the conversion of all convertible securities
then outstanding, would exceed the total number of shares of Stock then
authorized by the Company's Articles.

               Adjustment of Stock Purchase Price and Number of Shares.  Upon
               -------------------------------------------------------
each adjustment of the Stock Purchase Price as provided in Section 3, the holder
of this Warrant shall thereafter be entitled to purchase, at the Stock Purchase
Price resulting from such adjustment, the number of shares (calculated to the
nearest tenth of a share) obtained by multiplying the Stock

                                       3.
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Purchase Price in effect immediately prior to such adjustment by the number of
shares purchasable pursuant hereto immediately prior to such adjustment and
dividing the product thereof by the Stock Purchase Price resulting from such
adjustment.

          Section Adjustment of Price upon Issuance of Stock.  If and whenever
                  ------------------------------------------
the Company shall issue or sell any shares of its Stock for a consideration per
share less than the Stock Purchase Price in effect at the time of such issue or
sale, then, forthwith upon such issue or sale the Stock Purchase Price shall be
adjusted (calculated to the nearest $.01) determined by multiplying the Stock
Purchase Price by a fraction, the numerator of which is the amount equal to the
sum of (a) the number of shares of Stock outstanding immediately prior to such
issue or sale multiplied by the Stock Purchase Price in effect prior to such
issuance or sale, and (b) the consideration, if any, received by the Company
upon such issue or sale, and the denominator of which is the amount equal to the
total number of shares of Stock outstanding immediately after such issue or sale
multiplied by the Stock Purchase Price in effect prior to such issuance or sale.
No adjustments of the Stock Purchase Price, however, shall be made in an amount
less than $.01 per share, but any such lesser adjustment shall be carried
forward and shall be made at the time and together with the next subsequent
adjustment which together with any adjustments so carried forward shall amount
to $.01 per share or more.

          For purposes of this Section 3, the following paragraphs (a) to (k),
inclusive, shall also be applicable:

                 Issuance of Rights or Options.  In case at any time the Company
                 -----------------------------
     shall in any manner grant (whether directly or by assumption in a merger or
     otherwise) any rights to subscribe for or to purchase, or any options for
     the purchase of, Stock or any stock or securities convertible into or
     exchangeable for Stock (such rights or options being herein called
     "Options", and such convertible or exchangeable stock or securities being
     herein called "Convertible Securities") whether or not such Options or the
     right to convert or exchange any such Convertible Securities are
     immediately exercisable, and the price per share for which Stock is
     issuable upon the exercise of such Options or upon conversion or exchange
     of such Convertible Securities (determined by dividing (i) the total
     amount, if any, received or receivable by the Company as consideration for
     the granting of such Options, plus the minimum aggregate amount of
     additional consideration payable to the Company upon the exercise of all
     such Options, plus, in the case of such Options which relate to Convertible
     Securities, the minimum aggregate amount of additional consideration, if
     any, payable upon the issue or sale of such Convertible Securities and upon
     the conversion or exchange thereof, by (ii) the total maximum number of
     shares of Stock issuable upon the exercise of such Options or upon the
     conversion or exchange of all such Convertible Securities issuable upon the
     exercise of such Options) shall be less than the Stock Purchase Price then
     in effect at the time of the granting of such Options, then the total
     maximum number of shares of Stock issuable upon the exercise of such
     Options or upon conversion or exchange of the total maximum amount of such
     Convertible Securities issuable upon the exercise of such Options shall be
     deemed to have been issued for such price per share as of the date of
     granting of such Options and thereafter shall be deemed to be outstanding.
     Except as otherwise provided in paragraph (c), no adjustment of the Stock
     Purchase Price shall be made upon the actual issue of

                                       4.
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     such Stock or of such Convertible Securities upon exercise of such Options
     or upon the actual issue of such Stock upon conversion or exchange of such
     Convertible Securities.

               Issuance of Convertible Securities.  In case the Company shall in
               ----------------------------------
     any manner issue (whether directly or by assumption in a merger or
     otherwise) or sell any Convertible Securities, whether or not the rights to
     exchange or convert thereunder are immediately exercisable, and the price
     per share for which Stock is issuable upon such conversion or exchange
     (determined by dividing (i) the total amount received or receivable by the
     Company as consideration for the issue or sale of such Convertible
     Securities, plus the minimum aggregate amount of additional consideration,
     if any, payable to the Company upon the conversion or exchange of all such
     Convertible Securities by (ii) the total number of shares of Stock into
     which all such Convertible Securities are convertible) shall be less than
     the Stock Purchase Price then in effect at the time of such issue or sale,
     then the total maximum number of shares of Stock issuable upon conversion
     or exchange of all such Convertible Securities shall be deemed to have been
     issued for such price per share as of the date of the issue or sale of such
     Convertible Securities and thereafter shall be deemed to be outstanding,
     provided that (i) except as otherwise provided in paragraph (c) below, no
     adjustment of the Stock Purchase Price shall be made upon the actual issue
     of such Stock upon conversion or exchange of such Convertible Securities,
     and (ii) if any such issue or sale of such Convertible Securities is made
     upon exercise of any Option to purchase any such Convertible Securities for
     which adjustments of the Stock Purchase Price have been or are to be made
     pursuant to other provisions of this Section 3, no further adjustment of
     the Stock Purchase Price shall be made by reason of such issue or sale.

               Change in Option Price or Conversion Rate.  Upon the happening of
               -----------------------------------------
     any of the following events, namely, if the purchase price provided for in
     any Option referred to in paragraph (a), the additional consideration, if
     any, payable upon the conversion or exchange of any Convertible Securities
     referred to in paragraph (a) or (b), or the rate at which any Convertible
     Securities referred to in paragraph (a) or (b) are convertible into or
     exchangeable for Stock shall change at any time (other than under or by
     reason of provisions designed to protect against dilution), the Stock
     Purchase Price in effect at the time of such event shall forthwith be
     readjusted to the Stock Purchase Price which would have been in effect at
     such time had such Options or Convertible Securities still outstanding at
     the time of such change originally provided for such changed purchase
     price, additional consideration or conversion rate, as the case may be, at
     the time initially granted, issued or sold; and on the expiration of any
     such Option or the termination of any such right to convert or exchange
     such Convertible Securities, the Stock Purchase Price then in effect
     hereunder shall forthwith be increased to the Stock Purchase Price which
     would have been in effect at the time of such expiration or termination had
     such Option or Convertible Security, to the extent outstanding immediately
     prior to such expiration or termination, never been issued, and the Stock
     issuable thereunder shall no longer be deemed to be outstanding.

     If the purchase price provided for in any such Option referred to in
     paragraph (a) or the rate at which any Convertible Securities referred to
     in paragraph (a) or (b) are convertible

                                       5.
<PAGE>

     into or exchangeable for Stock, shall be reduced at any time under or by
     reason of provisions with respect thereto designed to protect against
     dilution, then in case of the delivery of Stock upon the exercise of any
     such Option or upon conversion or exchange of any such Convertible
     Security, the Stock Purchase Price then in effect hereunder shall forthwith
     be adjusted to such respective amount as would have been obtained had such
     Option or Convertible Security never been issued as to such Stock and had
     adjustments been made upon the issuance of the shares of Stock delivered as
     aforesaid, but only if as a result of such adjustment the Stock Purchase
     Price then in effect hereunder is thereby reduced.

               Stock Dividends.  In case the Company shall declare a dividend or
               ---------------
     make any other distribution upon any stock of the Company payable in Stock,
     Options or Convertible Securities, any Stock, Options or Convertible
     Securities, as the case may be, issuable in payment of such dividend or
     distribution shall be deemed to have been issued or sold without
     consideration.

               Consideration for Stock.  In case any shares of Stock, Options or
               -----------------------
     Convertible Securities shall be issued or sold for cash, the consideration
     received therefor shall be deemed to be the amount received by the Company
     therefor, without deduction therefrom of any expenses incurred or any
     underwriting commissions or concessions paid or allowed by the Company in
     connection therewith. In case any shares of Stock, Options or Convertible
     Securities shall be issued or sold for a consideration other than cash, the
     amount of the consideration other than cash received by the Company shall
     be deemed to be the fair value of such consideration as determined by the
     Board of Directors of the Company, without deduction of any expenses
     incurred or any underwriting commissions or concessions paid or allowed by
     the Company in connection therewith.  The amount of consideration deemed to
     be received by the Company pursuant to the foregoing provisions of this
     paragraph (e) upon any issuance and/or sale, pursuant to an established
     compensation plan of the Company, to directors, officers or employees of
     the Company in connection with their employment of shares of Stock, Options
     or Convertible Securities, shall be increased by the amount of any tax
     benefit realized by the Company as a result of such issuance and/or sale,
     the amount of such tax benefit being the amount by which the Federal and/or
     State income or other tax liability of the Company shall be reduced by
     reason of any deduction or credit in respect of such issuance and/or sale.
     In case any Options shall be issued in connection with the issue and sale
     of other securities of the Company, together comprising one integral
     transaction in which no specific consideration is allocated to such Options
     by the parties thereto, such Options shall be deemed to have been issued
     without consideration. In case any shares of Stock, Options or Convertible
     Securities shall be issued in connection with any merger or consolidation
     in which the Company is the surviving corporation, the amount of
     consideration therefor shall be deemed to be the fair value as determined
     by the Board of Directors of the Company of such portion of the assets and
     business of the non-surviving corporation as such Board shall determine to
     be attributable to such Stock, Options or Convertible Securities, as the
     case may be. In the event of any consolidation or merger of the Company in
     which the Company is not the surviving corporation or in the event of any
     sale of all or substantially all of the assets of the Company for stock or
     other securities of

                                       6.
<PAGE>

     any corporation, the Company shall be deemed to have issued a number of
     shares of its Stock for stock or securities of the other corporation
     computed on the basis of the actual exchange ratio on which the transaction
     was predicated and for a consideration equal to the fair market value on
     the date of such transaction of such stock or securities of the other
     corporation, and if any such calculation results in adjustment of the Stock
     Purchase Price, the determination of the number of shares of Stock
     receivable under this Warrant immediately prior to such merger,
     consolidation or sale, for purposes of paragraph (i), shall be made after
     giving effect to such adjustment of the Stock Purchase Price.

               Record Date.  In case the Company shall take a record of the
               -----------
     holders of its Stock for the purpose of entitling them (i) to receive a
     dividend or other distribution payable in Stock, Options or Convertible
     Securities, or (ii) to subscribe for or purchase Stock, Options or
     Convertible Securities, then such record date shall be deemed to be the
     date of the issue or sale of the shares of Stock deemed to have been issued
     or sold upon the declaration of such dividend or the making of such other
     distribution or the date of the granting of such right of subscription or
     purchase, as the case may be.

               Treasury Shares.  The number of shares of Stock outstanding at
               ---------------
     any given time shall not include shares owned or held by or for the account
     of the Company, and the disposition of any such shares shall be considered
     an issue or sale of Stock for the purposes of this Section 3.

               Subdivision or Combination of Stock.  In case the Company shall
               -----------------------------------
     at any time subdivide its outstanding shares of Stock into a greater number
     of shares, the Stock Purchase Price in effect immediately prior to such
     subdivision shall be proportionately reduced, and conversely, in case the
     outstanding shares of Stock of the Company shall be combined into a smaller
     number of shares, the Stock Purchase Price in effect immediately prior to
     such combination shall be proportionately increased.

               Reorganization, Reclassification, Consolidation, Merger or Sale.
               ---------------------------------------------------------------
     If any capital reorganization or reclassification of the capital stock of
     the Company or any consolidation or merger of the Company with another
     corporation, or the sale of all or substantially all of its assets to
     another corporation shall be effected in such a way that holders of Stock
     shall be entitled to receive stock, securities or assets with respect to or
     in exchange for Stock, then, as a condition of such reorganization,
     reclassification, consolidation, merger or sale, lawful and adequate
     provisions shall be made whereby each holder of the Warrants shall
     thereafter have the right to receive upon the basis and upon the terms and
     conditions specified herein and in lieu of the shares of Stock of the
     Company immediately theretofore receivable upon the exercise of such
     Warrant or Warrants, such shares of stock, securities or assets (including
     cash) as may be issued or payable with respect to or in exchange for a
     number of outstanding shares of such Stock equal to the number of shares of
     such stock immediately theretofore so receivable had such reorganization,
     reclassification, consolidation, merger or sale not taken place, and in any
     such case appropriate provision shall be made with respect to the rights
     and interests of such holder to the end that the provisions hereof
     (including without limitation provisions for adjustments of the Stock
     Purchase Price) shall thereafter be applicable, as

                                       7.
<PAGE>

     nearly as may be, in relation to any shares of stock, securities or assets
     thereafter deliverable upon the exercise of such exercise rights (including
     an immediate adjustment, by reason of such reorganization or
     reclassification, of the Stock Purchase Price to the value for the Common
     stock reflected by the terms of such reorganization or reclassification if
     the value so reflected is less than the Stock Purchase Price in effect
     immediately prior to such reorganization or reclassification). In the event
     of a merger or consolidation of the Company as a result of which a greater
     or lesser number of shares of common stock of the surviving corporation are
     issuable to holders of Stock of the Company outstanding immediately prior
     to such merger or consolidation, the Stock Purchase Price in effect
     immediately prior to such merger or consolidation shall be adjusted in the
     same manner as though there were a subdivision or combination of the
     outstanding shares of Stock of the Company. The Company will not effect any
     such consolidation, merger or any sale of all or substantially all of its
     assets of properties, unless prior to the consummation thereof the
     successor corporation (if other than the Company) resulting from such
     consolidation or merger or the corporation purchasing such assets shall
     assume by written instrument executed and mailed or delivered to each
     holder of the Warrants at the last address of such holder appearing on the
     books of the Company, the obligation to deliver to such holder such shares
     of stock, securities or assets as, in accordance with the foregoing
     provisions, such holder may be entitled to receive.

               Notice of Adjustment.  Upon any adjustment of the Stock Purchase
               --------------------
     Price, then and in each such case, the Company shall give written notice
     thereof, by first class mail, postage prepaid, addressed to each holder of
     the Warrants at the address of such holder as shown on the books of the
     Company, which notice shall state the Stock Purchase Price resulting from
     such adjustment, setting forth in reasonable detail the method of
     calculation and the facts upon which such calculation is based.

               Stock to Be Reserved.  The Company will at all times reserve and
               --------------------
     keep available out of its authorized Stock or its treasury shares, solely
     for the purpose of issue upon the exercise of this Warrant as herein
     provided, such number of shares of Stock as shall then be issuable upon the
     exercise of this Warrant.  The Company covenants that all shares of Stock
     which shall be so issued shall be duly and validly issued and fully paid
     and nonassessable and free from all taxes, liens and charges with respect
     to the issue thereof, and, without limiting the generality of the
     foregoing, the Company covenants that it will from time to time take all
     such action as may be requisite to assure that the par value per share of
     the Stock is at all times equal to or less than the effective Stock
     Purchase Price.  The Company will take all such action as may be necessary
     to assure that all such shares of Stock may be so issued without violation
     of any applicable law or regulation, or of any requirements of any national
     securities exchange upon which the stock of the Company may be listed. The
     Company will not take any action which results in any adjustment of the
     Stock Purchase Price if the total number of shares of Stock issued and
     issuable after such action upon exercise of this Warrant would exceed the
     total number of shares of Stock then authorized by the Company's Articles
     of Incorporation.  The Company has not granted and will not grant any right
     of first refusal with respect to

                                       8.
<PAGE>

     shares issuable upon exercise of this Warrant, and there are no preemptive
     rights associated with such shares.

                    Other Notices.  If at any time:
                    -------------

                         the Company shall declare any cash dividend upon its

Stock or Common Stock;

                         the Company shall declare any dividend upon its Stock
or Common Stock payable in stock or make any special dividend or other
distribution to the holders of its Stock or Common Stock;

                         the Company shall offer for subscription pro rata to
the holders of its Stock or Common Stock any additional shares of stock of any
class or other rights;

                         there shall be any capital reorganization or
reclassification of the capital stock of the Company; or consolidate or merger
of the Company with, or sale of all or substantially all of its asset to,
another corporation;

                         there shall be a voluntary or involuntary dissolution,
liquidation or winding-up of the Company; or

                         there shall be an Initial Public Offering of Company
securities;

then, in any one or more of said cases, the Company shall give, by first class
mail, postage prepaid, addressed to the Holder of this Warrant at the address of
such Holder as shown on the books of the Company, (a) at least 20 days' prior
written notice of the date on which the books of the Company shall close or a
record shall be taken for such dividend, distribution or subscription rights or
for determining rights to vote in respect of any such reorganization,
reclassification, consolidation, merger, sale, dissolution, liquidation or
winding-up, and (b) in the case of any such reorganization, reclassification,
consolidation, merger, sale, dissolution, liquidation, winding-up or public
offering, at least 20 days' prior written notice of the date when the same shall
take place; provided, however, that the Holder shall make a best efforts attempt
to respond to such notice as early as possible after the receipt thereof. Any
notice given in accordance with the foregoing clause (a) shall also specify, in
the case of any such dividend, distribution or subscription rights, the date on
which the holders of Stock or Common Stock, as the case may be, shall be
entitled thereto. Any notice given in accordance with the foregoing clause (b)
shall also specify the date on which the holders of Stock shall be entitled to
exchange their Stock for securities or other property deliverable upon such
reorganization, reclassification, consolidation, merger, sale, dissolution,
liquidation, winding-up, conversion or public offering, as the case may be.

                    Certain Events.  If any change in the outstanding Stock or
                    --------------
Common Stock of the Company or any other event occurs as to which the other
provisions of this Section 3 are not strictly applicable or if strictly
applicable would not fairly protect the

                                       9.
<PAGE>

purchase rights of the Holder of the Warrant in accordance with such provisions,
then the Board of Directors of the Company shall make an adjustment in the
number and class of shares available under the Warrant, the Stock Purchase Price
or the application of such provisions, so as to protect such purchase rights as
aforesaid. The adjustment shall be such as will give the Holder of the Warrant
upon exercise for the same aggregate Stock Purchase Price the total number,
class and kind of shares as he would have owned had the Warrant been exercised
prior to the event and had he continued to hold such shares until after the
event requiring adjustment.

               Issue Tax.  The issuance of certificates for shares of Stock
               ---------
upon the exercise of the Warrant shall be made without charge to the Holder of
the Warrant for any issue tax (other than any applicable income taxes) in
respect thereof; provided, however, that the Company shall not be required to
pay any tax which may be payable in respect of any transfer involved in the
issuance and delivery of any certificate in a name other than that of the then
holder of the Warrant being exercised.

               Closing of Books.  The Company will at no time close its transfer
               ----------------
books against the transfer of any warrant or of any shares of Stock issued or
issuable upon the exercise of any warrant in any manner which interferes with
the timely exercise of this Warrant.

               No Voting or Dividend Rights; Limitation of Liability.  Nothing
               -----------------------------------------------------
contained in this Warrant shall be construed as conferring upon the Holder
hereof the right to vote or to consent or to receive notice as a shareholder of
the Company or any other matters or any rights whatsoever as a shareholder of
the Company.  No dividends or interest shall be payable or accrued in respect of
this Warrant or the interest represented hereby or the shares purchasable
hereunder until, and only to the extent that, this Warrant shall have been
exercised. No provisions hereof, in the absence of affirmative action by the
Holder to purchase shares of Stock, and no mere enumeration herein of the rights
or privileges of the Holder hereof, shall give rise to any liability of such
Holder for the Stock Purchase Price or as a shareholder of the Company, whether
such liability is asserted by the Company or by its creditors.

               Warrants Transferable.  Subject to compliance with applicable
               ---------------------
federal and state securities laws, this Warrant and all rights hereunder are
transferable, in whole or in part, without charge to the Holder hereof (except
for transfer taxes), upon surrender of this Warrant properly endorsed.  Each
taker and holder of this Warrant, by taking or holding the same, consents and
agrees that this Warrant, when endorsed in blank, shall be deemed negotiable,
and that the Holder hereof, when this Warrant shall have been so endorsed, may
be treated by the Company, at the Company's option, and all other persons
dealing with this Warrant as the absolute owner hereof for any purpose and as
the person entitled to exercise the rights represented by this Warrant, or to
the transfer hereof on the books of the Company any notice to the contrary
notwithstanding; but until such transfer on such books, the Company may treat
the registered owner hereof as the owner for all purposes.

               Modification and Waiver.  This Warrant and any provision hereof
               -----------------------
may be changed, waived, discharged or terminated only by an instrument in
writing signed by the Company and the Holder.

                                      10.
<PAGE>

               Notices.  Any notice, request or other document required or
               -------
permitted to be given or delivered to the Holder hereof or the Company shall be
delivered or shall be sent by certified mail, postage prepaid, to each such
Holder as its address as shown on the books of the Company or to the Company c/o
Falcon Technology Partners, L.P., 600 Dorset Road, Devon, PA 19333, or such
other address as either may from time to time provide to the other.

               Binding Effect on Successors.  This Warrant shall be binding
               ----------------------------
upon any corporation succeeding the Company by merger, consolidation or
acquisition of all or substantially all of the Company's assets. All of the
obligations of the Company relating to the Stock issuable upon the exercise of
this Warrant shall survive the exercise and termination of this Warrant. All of
the covenants and agreements of the Company shall inure to the benefit of the
successors and assigns of the Holder hereof.

               Descriptive Headings and Governing Law. The description headings
               --------------------------------------
of the several sections and paragraphs of this Warrant are inserted for
convenience only and do not constitute a part of this Warrant. This Warrant
shall be construed and enforced in accordance with, and the rights of the
parties shall be governed by, the laws of the State of Delaware.

               Lost Warrants.  The Company represents and warrants to the Holder
               -------------
hereof that upon receipt of evidence reasonably satisfactory to the Company of
the loss, theft, destruction, or mutilation of this Warrant and, in the case of
any such loss, theft or destruction, upon receipt of an indemnity reasonably
satisfactory to the Company, or in the case of any such mutilation upon
surrender and cancellation of such Warrant, the Company, at its expense, will
make and deliver a new Warrant, of like tenor, in lieu of the lost, stolen,
destroyed or mutilated Warrant.

               Fractional Shares.  No fractional shares shall be issued upon
               -----------------
exercise of this Warrant. The Company shall, in lieu of issuing any fractional
share, pay the holder entitled to such fraction a sum in cash equal to such
fraction multiplied by the then effective Stock Purchase Price.

          IN WITNESS WHEREOF, the Company has caused this Warrant to be duly
executed by its officer, thereunto duly authorized this _____th day of
November, 1996.

                                        GENOMICA CORPORATION, a Delaware
                                        corporation


                                        By:____________________________________
                                                    James L. Rathmann
                                        Title:  President

                                      11.