distortion theorems of plane quasiconformal mappings abstract the authors prove a conjecture on elliptic integrals and obtain sharp bounds for k r and k by using teichmuller s module theorem the authors obtain a distortion theorem of k quasiconformal mappings on the plane

second chern class of fano manifolds and anti canonical geometry let x be a fano manifold of picard number one we establish a lower bound for the second chern class of x in terms of its index and degree as an application if y is a n dimensional fano manifold with k y n 3 h for some ample divisor h we prove that h 0 y h ge n 2 moreover we show that the rational map defined by vert mh vert is birational for m ge 5 and the linear system vert mh vert is basepoint free for m ge 7 as a by product the pluri anti canonical systems of singular weak fano varieties of dimension at most 4 are also investigated

local convexity properties of quasihyperbolic balls in punctured space this paper deals with local convexity properties of the quasihyperbolic metric in the punctured space we consider convexity and starlikeness of the quasihyperbolic balls

new family of modal methods for calculating eigenvector derivatives a new family of modal methods for the calculation of eigenvector derivatives in non sell adjoint systems with a singular coefficient matrix is developed the family contains the modal and modified modal methods as a subset in the family the component of the mth eigenvector in the expansion of the derivative of the jth eigenvector is multiplied by various powers of the eigenvalue ratio j m thereby accelerating convergence the family of methods is applied to a sell adjoint example problem namely a cantilever beam whose root depth is used as the design variable to which the sensitivity of the first four mode shapes is sought

on the simultaneous generation of jets of the adjoint bundles abstract in this paper we investigate the problem of the simultaneous generation of r jets of the bundle x l m where l is an ample and globally generated line bundle on x the results work in arbitrary characteristics a similar problem is studied when x admits singularities

global generation of pluricanonical and adjoint linear series on smooth projective threefolds the purpose of this paper is to show how the cohomological techniques developed by kawamata reid shokurov and others lead to some effective and practical results of reider type on freeness of linear series on smooth complex projective threefolds in recent years there has been a great deal of interest in the geometric properties of pluricanonical and adjoint linear systems on surfaces and higherdimensional varieties among other things one wants to understand as explicitly as possible when the systems in question are base point free or very ample modem work in this area goes back to kodaira kod and bombieri bmb who studied pluricanonical maps of surfaces of general type more recently many of their results have emerged as special cases of a celebrated theorem of reider rdr reider uses vector bundle techniques to show that if b is a nef line bundle on a surface x such that b2 5 then kx b is globally generated unless there exist certain special curves c c x such that b c 1 he also obtains analogous criteria for kx b to be very ample a cohomological approach to these theorems based on miyaoka s vanishing theorem for zariski decompositions was given by sakai sak2

characterization of the 4 canonical birationality of algebraic threefolds for nonsingular projective threefolds x of general type whose geometric genus p g h 0 x k x is ge 5 the birationality of the fourth canonical map varphi 4 x phi 4k x was characterized by d q zhang and the first author in 2008 this paper aims at characterizing the birationality of varphi 4 x for those x with p g 4

decomposition properties of john domains in normed vector spaces abstract let e be a real normed vector space with dim e 2 in this paper we characterize john domains in e in terms of john domain decomposition property

seshadri constants and periods of polarized abelian varieties the purpose of this paper is to study the seshadri constants of abelian varieties consider a polarized abelian variety a l of dimension g over the field of complex numbers one can associate to a l a real number e a l its seshadri constant which in effect measures how much of the positivity of l can be concentrated at any given point of a the number e a l can be defined as the rate of growth in k of the number of jets that one can specify in the linear series oa kl alternatively one considers the blow up f x blx x x of x at a point x with exceptional divisor e x over x and defines e a l def sup e r f l ee is nef

dimension free quasiconformal distortion in n space most distortion theorems for k quasiconformal mappings in rn n 2 depend on both n and k in an essential way with bounds that become infinite as n tends to oo the present authors obtain dimension free versions of four well known distortion theorems for quasiconformal mappings namely bounds for the linear dilatation the schwarz lemma the e distortion theorem and the r1 quasisymmetry property of these mappings they show that the upper estimates they have obtained in each of these four main results remain bounded as n tends to oo with k fixed the proofs are based on a dimensioncancellation property of the function t h r 1 r t k t 0 k 0 where r t is the capacity of a teichmiiller extremal ring in rn the authors also prove a dimension free distortion theorem for the absolute cross ratio under k quasiconformal mappings of n from which several other distortion theorems follow as special cases

the quasiconformal subinvariance property of john domains in mathbb r n and its applications the main aim of this paper is to give a complete solution to one of the open problems raised by heinonen from 1989 concerning the subinvariance of john domains under quasiconformal mappings in mathbb r n as application the quasisymmetry of quasiconformal mappings is discussed

capacity densities and angular limits of quasiregular mappings it is shown that if a bounded quasiregular mapping of the unit ball bn c rn n 2 has a limit at b e abn through a set e c bn with b ee e then it has an angular limit at b provided that e is contained in an open cone c c bn with vertex b and that e is thick enough at b the thickness condition is expressed in terms of the n capacity density

highly accurate modal method for calculating eigenvector derivatives in viscous damping systems a highly accurate modal superposition method for computing complex eigenvector derivatives in viscous damp ing systems has been developed when higher modes are truncated the conventional modal superposition method cannot give an accurate solution and the errors may become significant in this paper calculating the derivatives is regarded as calculating the structural response to harmonic exciting using multiple modal accelerations and shifted poles highly accurate results would be obtained when only few modes are used all of the available modal superposition methods would be directly obtained from the proposed method numerical examples show that it achieves better calculation efficiency than all of the available modal methods and nelson s method when more than one eigenvector derivative is of interest moreover the presented method can be used to improve response calculations and substructure syntheses igenvector derivatives with respect to system parameters are widely used in structural design structural stability anal ysis finite element model updating and structural control since the earlier work of fox and kapoor 1 many methods have been developed 2 3 all of the available methods could be categorized into three groups modal method 1 3 4 direct method 1 4 and iter ation method 5 6 most of the iteration methods suffer from slow convergence rates and are less efficient recently ting6 improved the effectiveness of the method because the direct methods give out the exact solutions they are widely used however when the derivatives of a large number of eigenvectors are demanded the cal culation is very time consuming here the modal methods are more suitable the modal methods employ a modal superposition idea there fore the accuracy is dependent on the number of modes used in calculation when the complete set of eigenvectors is used the ex act solution could be obtained to guarantee the accuracy the clas sical modal method1 needs higher eigenvectors recently wang4 presented a modified modal method in which a modal acceleration type approach was used to approximate the contribution of trun cated higher modes therefore the modified modal method con verges faster than the classical method ma and hagiwara7 im proved the modified method with an appropriate shift value better convergence than that of the modified method is achieved and sys tems having zero eigenvalues can be directly analyzed to further improve the convergence the improved modified modal method8 10 and accurate modal superposition method9 have been proposed by several researchers the basic original idea of the aforementioned improved modal methods was found in the hu s book 11 the idea was used to improve the convergency of dynamic flexibility in series form for no damping systems all of the aforementioned methods were used for real eigen vectors for the cases of complex eigenvectors in viscous damp ing systems the three groups of methods were presented 12 13 the classical modal method for the complex eigenvectors which was similar to the method presented in ref 1 for real eigenvectors suffers from heavy modal truncation errors recently akgun14 presented a new family of modal methods for the calculation of the derivatives in non self adjo int systems the modal accelera tion approach was used to improve the convergence in this paper calculating the derivatives in viscous damping systems is regarded as calculating a structural response to a harmonic exciting using multiple modal accelerations and shifted poles a highly accurate modal method for calculating the derivatives has been developed there are clear mathematical and physical meanings in conduct ing the proposed method from which all of the available meth ods would be directly obtained furthermore fewer eigenvectors even only the specific eigenvector that is being considered are re quired for the predetermined accuracy as a result the method is more efficient in computation than akgun s method and nelson s method when more than one eigenvector derivative is of inter est numerical examples show that the proposed method is cor rect and drastically improves solution accuracy the method can directly be applied in systems with zero eigenvalues although the method is developed to calculate eigenvectors derivatives it can be used to improve response calculations and substructure syntheses

vector bundles of rank 2 and linear systems on algebraic surfaces let s be a smooth complex algebraic surface and let l be a divisor on s it is well known that the linear system il ksi where ks is the canonical divisor plays an important role in understanding the geometry of s several authors see for example 8 11 studied various properties of this system our paper treats the same subject but the point of view is different from the works mentioned above the philosophy underlying our approach is almost classical points on s more generally effective 0 cycles in special position with respect to il ksi see definition below contain information about the geometry of s this point of view was recently revived in 5 also 10 in fact this paper contains the technique of going from the effective 0 cycle z in special position with respect to il ksi to the geometry of s for the sake of completeness we give a definition and state a theorem which can be found in 5 10

seshadri constants on abelian varieties we show that on a complex abelian variety of dimension two or greater the seshadri constant of an ample line bundle is at least one moreover the seshadri constant is equal to one if and only if the polarized abelian variety splits as a product of a principally polarized elliptic curve and a polarized abelian subvariety of codimension one we also examine the case when the seshadri constant is not one and obtain lower bounds when the dimension of the abelian variety is small

practical complete modal space and its applications the orthogonality relationship between the column vectors of the equivalent matrix of high order modes and the mass and stiffness matrices does not exist this limitation reduces the computational efficiency in addition this nonorthogonality behavior may sometimes reduce the precision for certain applications of the pcms method to improve the orthogonality relationship between the equivalent high order mode matrix and the mass and stiffness matrices an optimal gram schmidt orthogonalization method can be used in the analysis

fujita s conjecture and frobenius amplitude we prove a version of fujita s conjecture in arbitrary characteristic generalizing results of k e smith our methods use the frobenius morphism but avoid tight closure theory we also obtain versions of fujita s conjecture for coherent sheaves with certain ampleness properties

sharp distortion theorems for quasiconformal mappings continuing their earlier work on distortion theory the authors prove some dimension free distortion theorems for k quasiconformal mappings in r for example one of the present results is the following sharp variant of the schwarz lemma if f is a k quasiconformal self mapping of the unit ball bn n 2 with f 0 0 then 41 k2ixik i if x i 411 k2ixil k for all x in b

derivatives of complex eigenvectors using nelson s method 6shyy w an adaptive grid method for navier stokes flow computation applied mathematics and computation vol 21 no 3 1987 pp 201 219 7jeng y n andliou s c modi edmultipleone dimensional adaptive grid method numerical heat transfer part b vol 15 no 2 1989 pp 241 247 8jeng y n and lee z s revisit to the modi ed muliple onedimensional adaptive grid method numerical heat transfer part b vol 29 no 3 1996 pp 305 323 9bockelie m j and smith r e an adaptive grid method for computing the high speed 3d viscous flow about a re entry vehicle aiaa paper 92 2685 june 1992 10yee h c and harten a implicit tvd schemes for hyperbolic conservation laws in curvilinear coordinates aiaa journal vol 25 no 2 1987 pp 266 274 11jeng y n and liou y c adaptive grid generation by elliptic equations with grid control at all of the boundaries numerical heat transfer part b vol 23 no 2 1993 pp 135 151

on the projective normality of double coverings over a rational surface abstract we study the projective normality of a minimal surface x which is a ramified double covering over a rational surface s with dim k s 1 in particular horikawa surfaces the minimal surfaces of general type with k x 2 2 p g x 4 are of this type up to resolution of singularities let be the covering map from x to s we show that the z 2 invariant adjoint divisors k x r a are normally generated where the integer r 3 and a is an ample divisor on s

on the subinvariance of uniform domains in banach spaces abstract suppose that e and e denote real banach spaces with dimension at least 2 that d e and d e are domains and that f d d is a homeomorphism in this paper we prove the following subinvariance property for the class of uniform domains suppose that f is a freely quasiconformal mapping and that d is uniform then the image f d 1 of every uniform subdomain d 1 in d under f is still uniform this result answers an open problem of vaisala in the affirmative

non annulation effective et positivite locale des fibres en droites amples adjoints we show how to use effective non vanishing to prove that seshadri constants of some ample divisors are bigger than 1 on smooth threefolds whose anticanonical bundle is nef or on fano varieties of small coindice we prove the effective non vanishing conjecture of ionescu kawamata in dimension 3 in the case of line bundles of high volume

comparison of several methods for calculating vibration mode shape derivatives four methods for the calculation of derivatives of vibration mode shapes eigenvectors with respect to design parameters are described these are finite difference method modal method a modified modal method and nelson s method the methods are implemented in a general purpose commercial finite element program and applied to the following test problems a cantilever beam and a stiffened cylinder with a cutout design variables are a beam tip mass a beam root height and specific dimensions of the cylinder model the methods are compared on the basis of central processor cp seconds required to obtain the derivatives and two of the methods are also evaluated for the rapidity of convergence data is presented showing the amount of cp time used to compute the first four eigenvector derivatives for each example problem a scalar measure of the error in the mode shape derivative is defined and numerical results illustrating the rapidity of convergence of the approximate derivative to the exact derivative are presented results indicate an advantage in using nelson s method because this method is exact and requires less cp time especially when derivatives with respect to several design variables are computed

a numerical criterion for very ample line bundles let x be a projective algebraic manifold of dimension n and let l be an ample line bundle over x we give a numerical criterion ensuring that the adjoint bundle kx l is very ample the sufficient conditions are expressed in terms of lower bounds for the intersection numbers l y over subvarieties y of x in the case of surfaces our criterion gives universal bounds and is only slightly weaker than i reider s criterion when dimx 3 and codimy 2 the lower bounds for l y involve a numerical constant which depends on the geometry of x by means of an iteration process it is finally shown that 2kx ml is very ample form 12n our approach is mostly analytic and based on a combination of hormander s l estimates for the operator lelong number theory and the aubin calabi yau theorem

natural frequency and mode shape sensitivities of damped systems part ii multiple natural frequencies abstract an efficient algorithm with proven numerical stability is derived for computation of eigenvalue and eigenvector derivatives of damped vibratory systems with multiple eigenvalues in the proposed method adjacent eigenvectors and orthonormal condition are used to compose an algebraic equation whose order is n m n m where n is the number of co ordinates and m the number of multiplicity of a multiple natural frequency the mode shape derivatives of the damped systems can be obtained by solving the algebraic equation the method can be consistently applied to both structural systems with structural design parameters and mechanical systems with lumped design parameters as an example of a structural system to demonstrate the theory of the proposed methods and its possibilities in the case of multiple eigenvalues the finite element model of the cantilever beam is considered and also a 5 dof mechanical system in the case of a non proportionally damped system the design parameter of the cantilever beam is its height and that of the 5 dof mechanical system is a spring

on birational geometry of minimal threefolds with numerically trivial canonical divisors for a minimal threefold x with k x equiv 0 and a nef and big weil divisor l on x we investigate the birational geometry inspired by l we prove that ml and k x ml give birational maps for all m ge 17 the result remains true under weaker assumption that l is big and has no stable base components

seshadri constants at very general points we study the local positivity of an ample line bundle at a very general point of a smooth projective variety we obtain a slight improvement of the result of ein kuchle and lazarsfeld

on mori s theorem for quasiconformal maps in the n space r fehlmann and m vuorinen proved in 1988 that mori s constant m n k for k quasiconformal maps of the unit ball in r n onto itself keeping the origin fixed satisfies m n k 1 when k 1 we give here an alternative proof of this fact with a quantitative upper bound for the constant in terms of elementary functions our proof is based on a refinement of a method due to g d anderson and m k vamanamurthy we also give an explicit version of the schwarz lemma for quasiconformal self maps of the unit disk some experimental results are provided to compare the various bounds for the mori constant when n 2

successive minima of line bundles abstract we introduce and study the successive minima of line bundles on proper algebraic varieties the first resp last minima are the width resp seshadri constant of the line bundle at very general points the volume of the line bundle is equivalent to the product of the successive minima for line bundles on toric varieties the successive minima are equivalent to the reciprocal of usual successive minima of the difference of the moment polytope

novel modal method for efficient calculation of complex eigenvector derivatives a novel modal superposition method is presented for calculating eigenvector derivatives in self adjoint or non self adjoint systems the method is especially appropriate for determination of derivatives of many eigenvectors and requires only one eigenvalue and its corresponding right and left eigenvectors two parameters for the eigenvalue under consideration are introduced to obtain a generic derivative formula which contains most of the available modal superposition methods as a branch matrices of the modified system are decomposed with available lower modes to avoid repeatedly solving equations for different eigenvalues the contribution of truncated higher modes is expanded in a continued product of a few matrices polynomials and one generalized power series whereby rapid convergence can be achieved easily even in the vicinity of the convergent boundary without additional computation cost all other modal superposition coefficients can be neglected intrinsically with the determination of introduced parameters but a simple condition for coefficients associated with lower order eigenvalues should be satisfied in a special case numerical examples show that the method is efficient and can give results comparable to the exact solutions the method is applicable to various damped systems and closed mode cases

positivity and complexity of ideal sheaves the problem of bounding the complexity of a polynomial ideal in terms of the degrees of its generators has attracted a great deal of interest in recent years results in this direction go back at least as far as the classical work 17 of hermann on the ideal membership problem and the effective nullstellensatz of brownawell 4 and kollar 21 marks a major recent advance with the development of computational algebraic geometry the question has taken on increasing importance and it came into particularly clear focus through the influential paper 3 of bayer andmumford more recently the theorem of 8 and 20 concerning regularity of powers raises the question of bounding the complexity of powers of an ideal and suggests that asymptotically the picture should become very clean the aim of the present paper is to examine some of the results and questions of 3 30 and 7 from a geometric perspective in the spirit of 12 our thesis is that much of this material is clarified and parts rendered transparent when viewed through the lenses of vanishing theorems and intersection theory specifically motivated by thework 25 26 of paolettiwe introduce an invariant s j thatmeasures in effect howmuchonehas to twist an idealj in order tomake

seshadri constants and fano manifolds in memory of meeyoung kim in this paper we give a lower bound of seshadri constants on smooth fano varieties more precisely we show that on a smooth fano manifold of dimension n whose anticanonical system is base point free seshadri constants of ample divisors are bounded from below by one over n 2 as a corollary we recover the earlier result on fano threefolds

a sharp lower bound for the canonical volume of 3 folds of general type let v be a smooth projective 3 fold of general type denote by k 3 a rational number the self intersection of the canonical sheaf of any minimal model of v one defines k 3 as the canonical volume of v assume p g v 2 we show that k 3 ge frac 1 3 which is a sharp lower bound then we classify those v with small volume we also give some new examples with p g 2 which have maximal canonical stability index finally we give an application to 4 folds of general type

the boundedness of degree of fano varieties with picard number one contents 0 introduction 1 rational curves 1 1 deformation theory of morphisms 1 2 free rational curves 1 3 the invariant d m 2 special subvarieties in fano varieties of large degree 2 1 the statement 2 2 a siegel type lemma 2 3 multiplicity subspaces 2 4 the product theorem part i 2 5 the product theorem part ii 2 6 the proof 3 the covering lemma 4 collections of subsets 4 1 base change and push forward 4 2 an example 4 3 universally open morphisms 4 4 flat families 5 proof of theorem a

restricted volumes and base loci of linear series we introduce and study the restricted volume of a divisor along a subvariety our main result is a description of the irreducible components of the augmented base locus by the vanishing of the restricted volume

on the adjunction mapping of very ample vector bundles of corank one let e be a very ample vector bundle of rank n 1 over a smooth complex projective variety x of dimension n 3 the structure of x e being known when k x det e 0 we investigate the structure of the adjunction mapping when 0 k x det e n

on irregular threefolds and fourfolds with numerically trivial canonical bundle we prove that for a smooth projective irregular threefold x with k x equiv 0 and a nef and big divisor l on x ml p gives a birational map for all m ge 3 and all p in mathrm pic 0 x we also use the same method to deal with fourfolds and prove that for a smooth projective irregular fourfold x with k x equiv 0 and an ample divisor l on x ml p gives a birational map for all m ge 5 and all p in mathrm pic 0 x these results are optimal

on positivity of line bundles on enriques surfaces we study linear systems on enriques surfaces we prove rationality of seshadri constants of ample line bundles on enriques surfaces and provide lower bounds on these numbers we show the nonexistence of k very ample line bundles on enriques surfaces of degree 4k 4 for k 1 thus answering an old question of ballico and sommese introduction in this note we answer a question posed by ballico and sommese 1 see also terakawa 14 concerning the existence of k very ample line bundles of degree 4k 4 on enriques surfaces we show that such line bundles exist if and only if k 0 and that in fact the degree of a k very ample line bundle on an enriques surface is subject to a much more restrictive bound theorem 2 4 this has strong consequences for the local positivity of line bundles on enriques surfaces we address this questions in section 3 in particular we show that seshadri constants of ample line bundles on enriques surfaces are always rational 1 auxiliary material and notation the basic reference for this paper is the monograph 6 by cossec and dolgachev here we briefly recall properties of enriques surfaces needed for our considerations first of all an enriques surface is a surface y of kodaira dimension zero with no differential forms in particular ho ky 0 and the canonical bundle ky is a 2torsion element in pico y i e 2ky oy to alleviate notation it is convenient to use the following convention in the sequel we make frequent use of vanishing theorems and statements on adjoint line bundles since the canonical divisor ky is numerically trivial the adjoint line bundle ky l has the same numerical properties as l in particular if l is nef and big ample then so is ky l by the nakai moishezon criterion so in order to get vanishing statements for l we apply vanishing theorems to ky l and use the fact that 2ky is trivial in the sequel we do so without comment and hope to cause no confusion this way received by the editors june 1 2000 2000 mathematics subject classification primary 14j28 secondary 14c20 14e25

irreducibility brill noether loci and vojta s inequality this paper deals with generalizations of hilbert s irreducibility theorem the classical hilbert irreducibility theorem states that for any cover f of the projective line defined over a number field k there exist infinitely many k rational points on the projective line such that the fiber of f over p is irreducible over k in this paper we consider similar statements about algebraic points of higher degree on curves of any genus we prove that hilbert s irreducibility theorem admits a natural generalization to rational points on an elliptic curve and thus via a theorem of abramovich and harris to points of degree 3 or less on any curve we also present examples that show that this generalization does not hold for points of degree 4 or more these examples come from an earlier geometric construction of debarre and fahlaoui some additional necessary facts about this construction can be found in the appendix provided by debarre we exhibit a connection between these irreducibility questions and the sharpness of vojta s inequality for algebraic points on curves in particular we show that vojta s inequality is not sharp for the algebraic points arising in our examples

primitive higher order embeddings of abelian surfaces the aim of this note is to study higher order embeddings of abelian surfaces de nedby primitive line bundles in recent years several concepts of higher order embeddings have been studied in particular k spannedness k very ampleness and k jet ampleness see 7 for refer ences on this topic recall that a line bundle lon a smooth projective variety xis called k jet ample if for any choice of distinct points x

sensitivity analysis methods for coupled acoustic structural systems part i modal sensitivities an analytical method is proposed for calculating the sensitivities of the eigenvalues and eigenvectors of coupled acoustic structural systems for the purpose of reducing vehicle interior noise the concept of the left and right eigenvectors with regard to the eigenvalue problems of coupled systems is presented first and four propositions concerning this concept are then proved based on these propositions the formulations for the eigenvalue and eigenvector sensitivity analysis of coupled systems are obtained it is shown that the new method provides better convergence than the modal method and modified modal method extensions of these methods to coupled systems and it achieves better calculation efficiency than the extended nelson s method when more than one eigenvector is being considered the theoretical results and computation equations are verified through application of the method to a coupled acoustic box structure and an actual vehicle interior noise problem

tilt stability vanishing theorems and bogomolov gieseker type inequalities abstract we investigate the tilt stability of stable sheaves on projective varieties with respect to certain tilt stability conditions depends on two parameters constructed by bridgeland 11 see also 1 6 5 for a stable sheaf we give effective bounds of these parameters such that the stable sheaf is tilt stable these allow us to prove new vanishing theorems for stable sheaves and an effective serre vanishing theorem for torsion free sheaves using these results we also prove bogomolov gieseker type inequalities for the third chern character of a stable sheaf on p 3

accelerated subspace iteration for eigenvector derivatives an accelerated subspace iteration method for calculating eigenvector derivatives has been developed factors affecting the effectiveness and the reliability of the subspace iteration are identified and effective strategies concerning these factors are presented the method has been implemented and the results of a demonstration problem are presented

norm inequalities for vector functions abstract we study vector functions of r n into itself which are of the form x g x x where g 0 0 is a continuous function and call these radial functions in the case when g t t c for some c r we find upper bounds for the distance of image points under such a radial function some of our results refine recent results of l maligranda and s s dragomir in particular we study quasiconformal mappings of this simple type and obtain norm inequalities for such mappings

seshadri exceptional foliations the maximal seshadri number l of an ample line bundle l on a smooth projective variety x measures the local positivity of the line bundle l at a general point of x by refining the method of ein kuchle lazarsfeld lower bounds on l are obtained in terms of ln n dim x for a class of varieties the main idea is to show that if a certain lower bound is violated there exists a non trivial foliation on the variety whose leaves are covered by special curves in a number of examples one can show that such foliations must be trivial and obtain lower bounds for l the examples include the hyperplane line bundle on a smooth surface in 3 and ample line bundles on smooth threefolds of picard number 1

a frobenius variant of seshadri constants we define and study a version of seshadri constant for ample line bundles in positive characteristic we prove that lower bounds for this constant imply the global generation or very ampleness of the corresponding adjoint line bundle as a consequence we deduce that the criterion for global generation and very ampleness of adjoint line bundles in terms of usual seshadri constants holds also in positive characteristic

efficient computation of many eigenvector derivatives using dynamic flexibility method a new approach for computing eigenvector derivatives with repeated eigenvalues of a complex structural system has been successfully developed this method utilizes a dynamic flexibility technique unlike other published methods this method requires one only to solve the system linear algebraic equations once regardless of the number of eigenvector derivatives needed to be computed tremendous computer time can be saved using this method theoretical derivation of this method is presented numerical examples are also presented to verify the analysis this method can be a powerful tool for the design engineer to compute many eigenvector derivatives of a large complex structural system

examples of smooth non general type surfaces in p4 smooth projective varieties with small invariants have received renewed interest in recent years primarily due to the fine study of the adjunction mapping now through the effort of several mathematicians a complete classification of smooth surfaces in bbb p 4 has been worked out up to degree 10 and a partial one is available in degree 11 on the other side recently ellingsrud and peskine have proved hartshorne s conjecture that there are only finitely many families of smooth surfaces in bbb p 4 not of general type it is believed that the degree of the smooth non general type surfaces in bbb p 4 should be less than or equal to 15 the aim of this paper is to provide a series of examples of smooth surfaces in bbb p 4 not of general type in degrees varying from 12 up to 14 and to describe their geometry by using mainly syzygies and liaison techniques we construct the following families of surfaces begin enumerate item minimal proper elliptic surfaces of degree 12 and sectional genus pi 13 item two types of non minimal proper elliptic surfaces of degree 12 and sectional genus pi 14 item non minimal k3 surfaces of degree 13 and sectional genus 16 and item non minimal k3 surfaces of degree 14 and sectional genus 19 1991 mathematics subject classification 14m07 14j25 14j26 14j28 14c05

monotonicity theorems and inequalities for the complete elliptic integrals we prove monotonicity properties of certain combinations of complete elliptic integrals of the first and second kind k and e these results lead to sharp symmetrical bounds for k and e which improve recently discovered inequalities

positivity of line bundles on general blow ups of abelian surfaces abstract let s l s be a polarized abelian surface and let m c l s i 1 r e i be a line bundle on bl r s where bl r s s is the blow up of s at r general points with exceptional divisors e 1 e r in this paper we provide a criterion for k very ampleness of m also we deal with the case when s is an arbitrary surface of picard number one with a numerically trivial canonical divisor

families of nodal curves on projective threefolds and their regularity via postulation of nodes the main purpose of this paper is to introduce a new approach to study families of nodal curves on projective threefolds precisely given x a smooth projective threefold e a rank two vector bundle on x l a very ample line bundle on x and k 0 0 integers and denoted by v e l k the subscheme of p h 0 e l k parametrizing global sections of e l k whose zero loci are irreducible and nodal curves on x we present a new cohomological description of the tangent space t s v e l k at a point s 2 v e l k this description enable us to determine effective and uniform upper bounds for which are linear polynomials in k such that the family v e lk is smooth and of the expected dimension regular for short the almost sharpness of our bounds is shown by some interesting examples furthermore when x is assumed to be a fano or a calaby yau threefold we study in detail the regularity property of a point s 2 v e lk related to the postulation of the nodes of its zero locus c v s x roughly speaking when the nodes of c are assumed to be in general position either on x or on an irreducible divisor of x having at worst log terminal singularities or to lie on a l c i and subcanonical curve in x we find upper bounds onwhich are respectively cubic quadratic and linear polynomials in k ensuring the regularity of v e l k at s finally when x p 3 we also discuss some interesting geometric properties of the curves given by sections parametrized by v e ox k

seshadri constants of quartic surfaces by seshadri s criterion l is ample if and only if e l 0 recent interest in seshadri constants derives on the one hand from their application to adjoint linear systems in fact a lower bound on the seshadri constant of l gives a bound on the number of jets that the adjoint line bundle ox kx l separates see 2 and 3 on the other hand seshadri constants are very interesting invariants of polarized varieties in their own right it is this second aspect that we investigate in the present paper specifically consider a smooth surface x ip and think of the projective embedding as fixed we then simply write