generating a residual intersection let i be an ideal of height g 0 in a commutative noetherian ring r and let 2i be a proper sub ideal of i generated by 3 g elements if the ideal j 21 i has height at least s then j is called an s residual intersection of i see artin and nagata 1 huneke 19 or huneke and ulrich 22 the case s g corresponds to the theory of linkage and is well understood at least from the homolo cal point of view the cornerstone of this theory is that if i is perfect then a free resolution of r j can be produced from a free resolution of r z and the koszul complex on a set of generators of cu very little is known about resolutions of s residual intersections for s g a few special cases have been resolved s 10 301 and the end of the resolution or in other words a set of generators for the canonical module of r j has been described 22 however in general even the generators of j remain unknown here we show that j can be approximated by a sum of links of i if s g 1 and we give conditions under which this approximation in fact gives a full set of generators of j since these generators arise from comparison maps from koszul complexes to known resolutions at least assuming that the resolution of r i is in some sense known it is feasible to count them compute their degrees in the graded case or even to give explicit formulas for them after stating our main results theorem 2 15 and 2 16 and corollary 2 18 precisely in section 2 we lay out the argument in sections 3 4 and 5 in section 6 we are concerned with the question of when a g t 1 residual intersection j is

algebra structures on resolutions of rings defined by grade four almost complete intersections abstract let r m k be a local ring in which 2 is a unit and let j be an indeal in r the minimal r free resolution of r j is called a dg algebra if it has the structure of an associative differential graded commutative algebra over r if j is a grade four almost complete intersection ideal in r then j is necessarily linked to a grade four gorenstein ideal i by a grade four complete intersection k it is well known that the minimal r free resolutions of r i and r k admit dg algebra structures in this paper we show that if w denotes the image of the map torr1 r k k torr1 r i k and w2 0 for example if k m i then the minimal r free resolution of s r j has a dg algebra structure in the case where the ring r is regular local and k m i we prove that the poincare series pns t of every finitely generated s module n is rational and the ring s satisfies the eisenbud conjecture

an alternating matrix and a vector with application to aluffi algebras abstract let x be a generic alternating matrix t be a generic row vector and j be the ideal pf 4 x i 1 tx we prove that j is a perfect gorenstein ideal of grade equal to the grade of pf 4 x plus two this result is used by ramos and simis in their calculation of the aluffi algebra of the module of derivations of the homogeneous coordinate ring of a smooth projective hypersurface we also prove that j defines a domain or a normal ring or a unique factorization domain if and only if the base ring has the same property the main object of study in the present paper is the module n which is equal to the column space of x calculated mod pf 4 x the module n is a self dual maximal cohen macaulay module of rank two furthermore j is a bourbaki ideal for n the ideals which define the homogeneous coordinate rings of the plucker embeddings of the schubert subvarieties of the grassmannian of planes are used in the study of the module n

cusp development in hele shaw flow with a free surface free surface flow in a hele shaw cell is considered it has been known for some time that when the fluid region is contracting a finite time blow up can occur in which a cusp forms in the free surface the solution does not exist beyond the time of blow up examples are presented of this blow up and also of a new process in which a cusp of a different type forms in the free surface but after which the solution continues to exist after a transformation of the dependent variable the pressure the new cusps are related to permissible singularities in the free boundary of the obstacle problem

classification of the tor algebras of codimension four almost complete intersections let r m k be a local ring in which 2 is a unit assume that every element of k has a square root in k we classify the algebras tor r r j k as j varies over all grade four almost complete intersection ideals in r the analogous classification has already been found when j varies over all grade four gorenstein ideals 21 and when j varies over all ideals of grade at most three 5 30 the present paper makes use of the classification in 21 of the tor algebras of codimension four gorenstein rings as well as the usually nonminimal dg algebra resolution of a codimension four almost complete intersection which is produced in 25 and 26

a typed lambda calculus with intersection types intersection types are well known to type theorists mainly for two reasons firstly they type all and only the strongly normalizable lambda terms secondly the intersection type operator is a meta level operator that is there is no direct logical counterpart in the curry howard isomorphism sense in particular its meta level nature implies that it does not correspond to the intuitionistic conjunction the intersection type system is naturally a type inference system system a la curry but the meta level nature of the intersection operator does not allow to easily design an equivalent typed system system a la church there are many proposals in the literature to design such systems but none of them gives an entirely satisfactory answer to the problem in this paper we will review the main results in the literature both on the logical interpretation of intersection types and on proposed typed lambda calculi the core of this paper is a new proposal for a true intersection typed lambda calculus without any meta level notion namely any typable term in the intersection type inference has a corresponding typed term which is the same as the untyped term by erasing the type decorations and the typed term constructors with the same type and vice versa the main idea is to introduce a relevant parallel term constructor which corresponds to the intersection type constructor in such a way that terms in parallel share the same resources that is the same context of free typed variables three rules allow us to generate all typed terms the first two rules application and lambda abstraction are performed on all the components of a parallel term in a synchronized way finally via the third rule of local renaming once a free typed variable is bounded by lambda abstraction each of the terms in parallel can do its local renaming with type refinement of that particular resource

on parametric gevrey asymptotics for some nonlinear initial value cauchy problems abstract we study a nonlinear initial value cauchy problem depending upon a complex perturbation parameter with vanishing initial data at complex time t 0 and whose coefficients depend analytically on t near the origin in c 2 and are bounded holomorphic on some horizontal strip in c w r t the space variable this problem is assumed to be non kowalevskian in time t therefore analytic solutions at t 0 cannot be expected in general nevertheless we are able to construct a family of actual holomorphic solutions defined on a common bounded open sector with vertex at 0 in time and on the given strip above in space when the complex parameter belongs to a suitably chosen set of open bounded sectors whose union form a covering of some neighborhood of 0 in c these solutions are achieved by means of laplace and fourier inverse transforms of some common depending function on c r analytic near the origin and with exponential growth on some unbounded sectors with appropriate bisecting directions in the first variable and exponential decay in the second when the perturbation parameter belongs to moreover these solutions satisfy the remarkable property that the difference between any two of them is exponentially flat for some integer order w r t with the help of the classical ramis sibuya theorem we obtain the existence of a formal series generally divergent in which is the common gevrey asymptotic expansion of the built up actual solutions considered above

intersection types and lambda models invariance of interpretation by conversion is one of the minimal requirements for any standard model for the calculus with the intersection type systems being a general framework for the study of semantic domains for the calculus the present paper provides a syntactic characterisation of the above mentioned requirement in terms of characterisation results ibr intersection type assignment systems instead of considering conversion as a whole reduction and expansion will be considered separately not only for usual computational rules like but also for a number of relevant restrictions of those characterisations will be also provided for intersection filter structures that are indeed models

long time existence for a slightly perturbed vortex sheet consider a flat two dimensional vortex sheet perturbed initially by a small analytic disturbance by a formal perturbation analysis moore derived an approximate differential equation for the evolution of the vortex sheet we present a simplified derivation of moore s approximate equation and analyze errors in the approximation the result is used to prove existence of smooth solutions for long time if the initial perturbation is of size and is analytic in a strip m existence of a smooth solution of birkhoff s equation is shown for time t k2p if is sufficiently small with 1 as 0 for the particular case of sinusoidal data of wave length and amplitude e moore s analysis and independent numerical results show singularity development at time tc log o log log our results prove existence for t log if is sufficiently small with k 1 as 0 thus our existence results are nearly optimal

existence and uniqueness for a class of nonlinear higher order partial differential equations in the complex plane we prove existence and uniqueness results for nonlinear third order partial differential equations of the form

algebra structures on some canonical resolutions the study of algebra structures on finite free resolutions of cyclic modules begins with buchsbaum and eisenbud b el the classes of cyclic modules whose minimal resolutions are known to admit an algebra structure include the residue field gu complete intersections koszul complex modules of homological dimension atmost 3 b el gorenstein of codimension four k m and herzog algebras k m23 avramov al gave examples to show that there are cyclic modules whose minimal resolutions do not admit an algebra structure let r be a noetherian local ring with maximal ideal m in this paper we construct algebra structures on the minimal resolutions of two classes of cyclic modules r i namely when z is of the form jk where j is an ideal generated by a regular sequence and when z is the ideal of maximal minors of a generic n x m matrix provided r contains the rationals in al avramov defined certain obstructions to the existance of an algebra structure on the minimal resolution of a module and then produced modules with non zero obstructions the general question is whether the vanishing of these obstructions is also sufficient for the existence of a minimal algebra resolution of a cyclic module when z is an ideal generated by a regular sequence in r and m r z for any positive integer k then these obstructions are all zero therefore avramov and schlessinger asked whether the minimal resolutions of r z admit an algebra structure corollary 3 6 of this paper provides an affirmative answer to this question

zero viscosity limit for analytic solutions of the navier stokes equation on a half space i existence for euler and prandtl equations this is the first of two papers on the zero viscosity limit for the incompressible navier stokes equations in a half space in this paper we prove short time existence theorems for the euler and prandtl equations with analytic initial data in either two or three spatial dimensions the main technical tool in this analysis is the abstract cauchy kowalewski theorem for the euler equations the projection method is used in the primitive variables to which the cauchy kowalewski theorem is directly applicable for the prandtl equations cauchy kowalewski is applicable once the diffusion operator in the vertical direction is inverted

resonance theory for schrodinger operators resonances which result from perturbation of embedded eigenvalues are studied by time dependent methods a general theory is developed with new and weaker conditions allowing for perturbations of threshold eigenvalues and relaxed fermi golden rule the exponential decay rate of resonances is addressed its uniqueness in the time dependent picture is shown in certain cases the relation to the existence of meromorphic continuation of the properly weighted green s function to time dependent resonance is further elucidated by giving an equivalent time dependent asymptotic expansion of the solutions of the schrodinger equation

the minimal resolution of a codimension four almost complete intersection is a dg algebra abstract let r m k be a commutative noetherian local ring in which two is a unit we prove that if j is a five generated grade four perfect ideal in r then the minimal resolution of r j by free r modules is an associative differential graded commutative algebra this result extends and completes the work in j algebra 159 1993 1 46 where the conclusion is shown to hold provided certain technical conditions on tor are satisfied the multiplication on the resolution of r j is constructed using appropriate higher order multiplication on the resolution of r i where i is a gorenstein ideal which is linked to j

huneke ulrich almost complete intersections of cohen macaulay type two abstract let r m k be a commutative noetherian local ring n 2 an integer x a 2n 1 2n 1 alternating matrix with entries from m y a 1 2n 1 matrix with entries from m i the ideal i i1 yx and a the quotient ring r i assume that the grade of i is at least 2n in this case i is a perfect ideal of grade equal to 2n and i is minimally generated by 2n 1 elements we prove that the minimal resolution of a by free r modules is a dg algebra furthermore we identify the algebra torr a k and prove that if r is regular and char k 0 or n 2 2 char k then the poincare series pma z i 0 dimk torai m k zi is a rational function for every finitely generated a module m as a consequence we deduce that if the projective dimension of m is infinite then eventually the betti numbers of m form an increasing sequence with strong exponential growth

a nonlinear approximation for vortex sheet evolution and singularity formation abstract the evolution of a vortex sheet in two dimensional incompressible inviscid flow is governed by the integro differential equation of birkhoff rott we derive a simple approximation for vortex sheet evolution consisting of a system of four first order differential equations this approximate system has the advantage of involving only local operators the errors in the approximation are shown to be relatively small even if the sheet has infinite curvature at a point for the approximate equations exact similarity solutions exhibiting singularity formation are constructed

existence uniqueness analyticity and borel summability for boussinesq equations through borel summation methods we analyze the boussinesq equations for coupled fluid velocity and temperature fields 1 ut u p u u ae2 f t u we prove that an equivalent system of integral equations in the borel variable p r dual to 1 t has a unique solution in a class of exponentially bounded functions implying the existence of a classical solution to 1 in a complex t region that includes a real positive time axis segment for analytic initial data and forcing it is shown that the solution is borel summable implying that formal series in powers of t is gevrey 1 asymptotic and within the time interval of existence the solution remains analytic with the same analyticity strip width as the initial data and forcing we also determine conditions on the integral equation solution that improve the estimate for existence time

zero viscosity limit for analytic solutions of the navier stokes equation on a half space ii construction of the navier stokes solution this is the second of two papers on the zero viscosity limit for the incompressible navier stokes equations in a half space in either 2d or 3d under the assumption of analytic initial data we construct solutions of navier stokes for a short time which is independent of the viscosity the navier stokes solution is constructed through a composite asymptotic expansion involving the solutions of the euler and prandtl equations which were constructed in the first paper plus an error term this shows that the navier stokes solution goes to an euler solution outside a boundary layer and to a solution of the prandtl equations within the boundary layer the error term is written as a sum of first order euler and prandtl corrections plus a further error term the equation for the error term is weakly nonlinear its linear part is the time dependent stokes equation this error equation is solved by inversion of the stokes equation through expressing the solution as a regular euler like part plus a boundary layer prandtl like part the main technical tool in this analysis is the abstract cauchy kowalewski theorem

intersection types a la church in this paper we present a fully typed calculus based on the intersection type system discipline which is a counterpart a la church of the type assignment system as invented by coppo and dezani the relationship between and the intersection type assignment system is the standard isomorphism between typed and type assignment system and so the typed language inherits from the untyped system all the good properties like subject reduction and strong normalization moreover both type checking and type reconstruction are decidable

poincare series of modules over local rings of small embedding codepth or small linking number abstract let s n k be a commutative noetherian local ring and m be a finitely generated s module then the poincare series of m is rational if any of the following holds edim s depth s 3 edim s depth s 4 and s is gorenstein s is one link from a complete intersection s is two links from a complete intersection and s is gorenstein to prove this result we assume without loss of generality that s r i with r m regular local and the key to the argument is to produce a factorization of the canonical map r s as a composition of a complete intersection r c with a golod map c s this is accomplished by invoking a theorem of avramov and backelin once one has existence of a dg algebra structure on a minimal r free resolution of s together with detailed knowledge of the structure of the induced homology algebra tor r s k h k s linkage theory provides the main technical tool for this analysis

a matrix of linear forms which is annihilated by a vector of indeterminates abstract let r k t 1 t f be a standard graded polynomial ring over the field k and be an f g matrix of linear forms from r where 1 g f assume t 1 t f is 0 and that grade i g is exactly one short of the maximum possible grade we resolve r r i g prove that r has a g linear resolution record explicit formulas for the h vector and multiplicity of r and prove that if f g is even then the ideal i g is unmixed furthermore if f g is odd then we identify an explicit generating set for the unmixed part i g unm of i g resolve r i g unm and record explicit formulas for the h vector of r i g unm the rings r i g and r i g unm automatically have the same multiplicity these results have applications to the study of the blow up algebras associated to linearly presented grade three gorenstein ideals

boundedness versus periodicity over commutative local rings over commutative graded local artinian rings examples are constructed of periodic modules of arbitrary minimal period and modules with bounded betti numbers which are not eventually periodic they provide counterexamples to a conjecture of d eisenbud that every module with bounded betti numbers over a commutative local ring is eventually periodic of period 2 it is proved however that the conjecture holds over rings of small length

the minimal free resolution of the migliore peterson rings in the case that the reflexive sheaf has even rank abstract letrbe a commutative noetherian ring and f gbe a homomorphism of freer modules where rank f fand rank g g fix an elementbg 1 g 1fand a generator g for gg the module action of f on fproduces the elementb1 g g bg 1 inf letjdenote the image ofb1 f r assume that gradej f g which is the largest grade possible and is attained in the generic case the idealjmay be interpreted as the defining ideal of the degeneracy locus of a regular section of a rankf greflexive sheaf it may also be interpreted as the order ideal of an element in a second syzygy module of rankf g also jmay be interpreted as the defining ideal for the symmetric algebra of a module of projective dimension two migliore and peterson have studied the idealjunm which is the unmixed part ofj under geometric hypotheses they have shown thatr junmis a cohen macaulay ring and they have resolved this ring furthermore iff gis odd thenjunmis a gorenstein ideal and is not equal toj on the other hand iff gis even thenjunm j in the present paper we produce the resolution ofr jby freer modules in the case thatf gis even and f g 2 is a unit inr our resolution is minimal whenever the data are local or homogeneous our resolution is built from the differential graded algebra f x1 xg d where the restriction ofdto f is the koszul complex associated tob1 f rand the degree two divided power variablesx1 xghave been adjointed in order to kill the cycles g 1f the acyclicity lemma is used to prove exactness ifg 1 then the idealjis equal to the huneke ulrich almost complete intersection ideali1 yx whereyis a 1 fmatrix andxis anf falternating matrix the resolution of this ideal is already known

the minimal free resolutions of the huneke ulrich deviation two gorenstein ideals structure theorems exist for gorenstein ideals of small grade a different parameter one can use for organizing ideals is deviation or complete intersection defect the deviation of the ideal i is the minimal number of generators of i minus the grade of i a deviation zero ideal is a complete intersection kunz s proved that there are no deviation one gorenstein ideals presently people are trying to find all deviation two gorenstein ideals see for example 3 a hypersurface section of a grade g 1 deviation two gorenstein ideal is a grade g deviation two gorenstein ideal we consider this to be a trivial example very few non trivial examples of deviation two gorenstein ideals are known the buchsbaum eisenbud structure theorem 2 describes all grade three gorenstein ideals in particular every deviation two grade three gorenstein ideal is generated by the maximal order pfaflians of a 5 x 5 alternating matrix no non trivial deviation two gorenstein ideals of even grade are known herzog and miller 3 have taken a step toward proving that all grade four deviation two gorenstein ideals are trivial let i be a grade four deviation two gorenstein ideal if i is a generic complete intersection and i i is cohenmacaulay then i is a hypersurface section the only known non trivial deviation 2 gorenstein ideals of grade at least four are the ideals of huneke and ulrich 4 which are the ideals studied in this paper for each integer s let y be a 1 x s matrix of indeterminates x be an s x s alternating matrix of indeterminates g be the product y x and ct be the sequence gp g let a be the ideal of

borel summability of the heat equation with variable coefficients abstract we prove borel summability in nonsingular directions of solutions of partial differential equations of the form u t a z u z z where a z is a quartic polynomial and the initial condition is analytic in the special case a z z we obtain the detailed resurgent structure even in such a simple case the structure of the singular manifolds is quite intricate

on gevrey solutions of threefold singular nonlinear partial differential equations abstract we study gevrey asymptotics of the solutions to a family of threefold singular nonlinear partial differential equations in the complex domain we deal with both fuchsian and irregular singularities and allow the presence of a singular perturbation parameter by means of the borel laplace summation method we construct sectorial actual holomorphic solutions which turn out to share a same formal power series as their gevrey asymptotic expansion in the perturbation parameter this result rests on the malgrange sibuya theorem and it requires to prove that the difference between two neighboring solutions is exponentially small what in this case involves an asymptotic estimate for a particular dirichlet like series