openness of versality via coherent functors we give a proof of openness of versality using coherent functors as an application we streamline artin s criterion for algebraicity of a stack we also introduce multi step obstruction theories employing them to produce obstruction theories for the stack of coherent sheaves the quot functor and spaces of maps in the presence of non atness

motivic bivariant characteristic classes let k0 v x k0 v x be the relative grothendieck group of varieties over x obj v x obj v with v vk qp resp v vcan the category of quasi projective algebraic resp compact complex analytic varieties over a base field k then we constructed the motivic hirzebruch class transformation ty k0 v x h x q y ty k0 v x h x q y in the algebraic context for k of characteristic zero with h x ch x h x ch x resp in the complex algebraic or analytic context with h x h2 bm x it unifies the well known three characteristic class transformations of singular varieties macpherson s chern class baum fulton macpherson s todd class and the l class of goresky macpherson and cappell shaneson in this paper we construct a bivariant relative grothendieck group k0 v x y k0 v x y for v vk qp resp vcan so that k0 v x pt k0 v x k0 v x pt k0 v x in the algebraic context with k of characteristic zero resp complex analytic context we also construct in the algebraic context in any characteristic two grothendieck transformations mcy ymot k0 vqp x y kalg x y z y and ty k0 vqp x y h x y q y ty k0 vqp x y h x y q y with kalg f kalg f the bivariant algebraic k theory of f perfect complexes and hh the bivariant operational chow groups or the even degree bivariant homology in the case k ck c evaluating at y 0y 0 we get a motivic lift t0t0 of fulton macpherson s bivariant riemann roch transformation kalg h q kalg h q the covariant transformations mcy k0 vqp x pt g0 x z y mcy k0 vqp x pt g0 x z y and ty k0 vqp x pt h x q y ty k0 vqp x pt h x q y agree for k of characteristic zero with our motivic chern and hirzebruch class transformations defined on k0 vqp x k0 vqp x finally evaluating at y 1y 1 for k of characteristic zero we get a motivic lift t 1t 1 of ernstrom yokura s bivariant chern class transformation f ch

a potential theory for the k curvature equation abstract in this paper we introduce a potential theory for the k curvature equation which can also be seen as a pde approach to curvature measures we assign a measure to a bounded upper semicontinuous function which is strictly subharmonic with respect to the k curvature operator and establish the weak continuity of the measure

rogue wave and a pair of resonance stripe solitons to kp equation abstract the rogue wave and a pair of resonance stripe solitons to kp equation are discovered first based on the bilinear method some lump solutions are obtained containing six parameters four of which must cater to the non zero conditions so as to insure the solution analytic and rationally localized second a one stripe soliton lump solution is presented and the interaction shows that the lump soliton can be drowned or swallowed by the stripe soliton conversely the lump soliton is spit out from the stripe soliton finally a new ansatz of combination of positive quadratic functions and hyperbolic functions is introduced and thus a novel nonlinear phenomenon is explored it is interesting that a rogue wave can be excited it is observed that the rogue wave possessing a peak wave profile arises from one of the resonance stripe solitons moves to the other and then disappears therefore a rogue wave can be generated by the interaction between the lump soliton and the pair of resonance stripe solitons however compared with classic rouge wave the dynamics of above nonlinear waves are quite different which are graphically demonstrated

fixed point theorems for compact multimaps on almost γ convex sets in generalized convex spaces abstract in this paper we introduce the concept of the strict kakutani multimap kkm property and investigate the fixed point problem for multimaps having this property on almost convex subsets of locally g convex uniform spaces our new fixed point theorem generalizes the well known fan glicksberg fixed point theorem and partially extends the himmelberg fixed point theorem its application to minimax theorem is also given

cohomology and base change for algebraic stacks we prove that cohomology and base change holds for algebraic stacks generalizing work of brochard in the tame case we also show that hom spaces on algebraic stacks are represented by abelian cones generalizing results of grothendieck brochard olsson lieblich and roth starr to accomplish all of this we prove that a wide class of relative ext functors in algebraic geometry are coherent in the sense of m auslander

monge ampere equations in big cohomology classes we define non pluripolar products of an arbitrary number of closed positive 1 1 currents on a compact kahler manifold x given a big 1 1 cohomology class on x i e a class that can be represented by a strictly positive current and a positive measure on x of total mass equal to the volume of and putting no mass on pluripolar sets we show that can be written in a unique way as the top degree self intersection in the non pluripolar sense of a closed positive current in we then extend kolodziedj s approach to sup norm estimates to show that the solution has minimal singularities in the sense of demailly if has l 1 e density with respect to lebesgue measure if is smooth and positive everywhere we prove that t is smooth on the ample locus of provided is nef using a fixed point theorem we finally explain how to construct singular kahler einstein volume forms with minimal singularities on varieties of general type

non simple semistable vector bundles over a curve let x be a non singular algebraic curve over c of genus g 2 let s 3 0 be the set of indecomposable semistable vector bundles over x of rank 3 and degree 0 in 21 we prove that non simple vector bundles in s 3 0 must have algebra of endomorphisms isomorphic to c t t2 c t t 3 o r c r s r s 2 in this paper we prove that if we fix the algebra of endomorphisms and make a further subdivision in the case c t t2 then there exists a moduli space mi for such vector bundles in s 3 0 for some i m i is a fine moduli space i e there exists a universal family parametrized by mg see theorems 6 and 9 mainly we use the universal extensions constructed in 3 and we prove that under a suitable equivalence relation these extensions define the required moduli spaces the equivalence relations are defined by considering the c c x c c x c and the gl 2 c action in sect 1 we recall from 2 the conditions for a vector bundle to have a particular algebra of endomorphisms in the following sections we construct the moduli spaces my

m lump solutions to a 3 1 dimensional nonlinear evolution equation abstract this paper aims at computing the m lump solutions which decay to a uniform state in all directions for a 3 1 dimensional nonlinear evolution equation these solutions are constructed by taking a long wave limit of the corresponding n soliton solutions obtained by direct methods the dynamic properties of m lump solutions describing multiple collisions of lumps are presented in addition we investigate the interaction between stripe solitons and lumps which is further discussed implying that lumps will be drowned or swallowed by the stripe solitons finally the dynamic properties of interactive wave solutions are graphically depicted by choosing the values of parameters

residue formulae vector partition functions and lattice points in rational polytopes we obtain residue formulae for certain functions of several vari ables as an application we obtain closed formulae for vector partition func tions and for their continuous analogs they imply an euler maclaurin sum mation formula for vector partition functions and for rational convex poly topes as well we express the sum of values of a polynomial function at all lattice points of a rational convex polytope in terms of the variation of the integral of the function over the deformed polytope institut fourier b p 74 38402 saint martin d heres cedex france e mail address mbrion fourier ujf grenoble fr ecole normale superieure 45 rue d ulm 75005 paris cedex 05 france e mail address vergne dmi ens fr

an extension of mehta theorem with applications abstract a remarkable fundamental theorem established by mehta plays an important role in proving existence of fixed points maximal elements and equilibria in abstract economies in this paper we extend himmelberg s measure of precompactness to the general setting of l c spaces and obtain a generalization of mehta s theorem as an application we develop some new fixed point theorems involving a kind of condensing mappings

hodge genera of algebraic varieties ii we study the behavior of hodge genera under algebraic maps we prove thatthemotivic c y genussatisfiesthe stratifiedmultiplicativeproperty whichshows how to compute the invariant of the source of a morphism from its values on varieties arising from the singularities of the map by considering morphisms to a curve we obtain a hodge theoretic version of the riemann hurwitz formula we also study the monodromy contributions to the y genus of a family of compact complex manifolds and prove an atiyah meyer type formula in the algebraic and analytic contexts this formula measures the deviation from multiplicativity of the y genus and expresses the correction terms as higher genera associated to the period map these higher gen era are hodge theoretic extensions of novikov higher signatures to analytic and alge braic settings characteristic class formulae of atiyah meyer type are also obtained by making use of saito s theory of mixed hodge modules

numerical characterization of the kahler cone of a compact kahler manifold the goal of this work is to give a precise numerical description of the kahler cone of a compact kahler manifold our main result states that the kahler cone depends only on the intersection form of the cohomology ring the hodge structure and the homology classes of analytic cycles if x is a compact kahler manifold the kahler cone k of x is one of the connected components of the set p of real 1 1 cohomology classes which are numerically positive on analytic cycles i e y p 0 for every irreducible analytic set y in x p dim y this result is new even in the case of projective manifolds where it can be seen as a generalization of the well known nakai moishezon criterion and it also extends previous results by campana peternell and eyssidieux the principal technical step is to show that every nef class which has positive highest self intersection numberx n 0 contains a kahler current this is done by using the calabi yau theorem and a mass concentration technique for monge ampere equations the main result admits a number of variants and corollaries including a description of the cone of numerically effective 1 1 classes and their dual cone another important consequence is the fact that for an arbitrary deformation x s of compact kahler manifolds the kahler cone of a very general fibre xt is independent of t i e invariant by parallel transport under the 1 1 component of the gauss manin connection

analytic geometry of complex superspaces a detailed account of the analytic geometry of complex superspaces is given in this paper several representability criteria and representability theorems are proved in particular the existence of a versal family of deformations parametrized by a complex superspace for any compact complex superspace is proved

universal families of extensions if x denotes a projective variety over a field k and jr and y coherent sheaves on x the vector space exti sr y parametrizes the extensions of f by v on x and there is a universal extension of p t by p y on xx exti y 5 such that for every k rational point u of exti ir y its restriction to x x u is just the extension represented by u moreover p p extk st v parametrizes the classes of nonsplitting extensions of 9 by y on x module k and there is a universal family of extensions of pt f by pf5 p 1 on x x p over p such that for every k rational point p of p its restriction to x x p represents just the class of extensions given by p it is the purpose of this paper not only to prove these two statements but to generalize them to the relative case of a flat projective morphism f x y of noetherian schemes they turn out to be a consequence of grothendieck s universal properties of vector bundles and projective bundles cp 2 section i 91 special cases of these results appeared several times in the literature to the best of my knowledge first in 5 lemma 3 11 and second in 6 lemma 2 41 the technical tool is the base change theory for relative ext sheaves which is outlined in section 1 in section 2 some relations between relative ext sheaves and families of extensions are given section 3 contains the construction of the universal family of extensions and section 4 the construction of the universal family of classes of nonsplitting extensions concerning the notation f x y means a flat projective morphism of noetherian schemes and r and ce coherent ox modules flat over y the proofs of sections 2 to 4 are more generally correct if only there is a base change theory for relative ext sheaves for example if one uses the base change results of 1 valid for arbitrary proper flat morphisms of complex spaces one gets the corresponding results in this case too 101 oozl 8693183 3 00

teichmuller spaces and torelli theorems for hyperkahler manifolds kreck and yang su recently gave counterexamples to a version of the torelli theorem for hyperkahlerian manifolds as stated by verbitsky we extract the correct statement and give a short proof of it we also revisit a few of its consequences some of which are given new shorter proofs and ask some questions

factorisation of generalised theta functions i we prove a version of factorisation relating the space of sections of theta bundles on the moduli spaces of parabolic rank 2 vector bundles on curves of genusg andg 1

breather lump and x soliton solutions to nonlocal kp equation abstract breather lump and x soliton solutions are presented via the hirota bilinear method to the nonlocal 2 1 dimensional kp equation derived from the alice bob system the resulting breather contains two cases one is the line breather and another is the normal breather both of which are different from the solutions of the classical 2 1 dimensional kp equation the x soliton is found with the long wave limit by some constraints to the parameters the lump solution is obtained in virtue of two methods one is as the long wave limit of breather theoretically the other is with the quadratic function method which can be guaranteed rationally localized in all directions in the space under some constraints of the parameters by choosing specific values of the involved parameters the dynamic properties of some breather lump solutions to nonlocal kp equation are plotted as illustrative examples

ricci flow on quasi projective manifolds we consider the kahler ricci flow on complete finite volume metrics that live on the complement of a divisor in a compact kahler manifold x assuming certain spatial asymptotics on the initial metric we compute the singularity time in terms of cohomological data on x we also give a sufficient condition for the singularity if there is one to be type ii

explicit solutions of the bogoyavlensky konoplechenko equation by means of the generalized direct method a relationship is constructed between the new solutions and the old ones of the bogoyavlensky konoplechenko equation based on the relationship a new solution is obtained by using a given solution of the equation the symmetry is also obtained for the bk equation then we get the reductions using the symmetry and give some exact solutions of the bk equation

fixed point theorems for condensing multimaps on locally g convex spaces abstract in this paper we investigate the fixed point problem for condensing multimaps on locally g convex spaces instead of the usual locally convex topological vector spaces we show that every condensing closed self multimap that has convex values on a nonempty complete convex subset of a locally g convex space has a fixed point some fixed point results for condensing multimaps which have lower semicontinuous l s c cores and applications to abstract economy are also presented

the complex monge ampere type equation on compact hermitian manifolds and applications abstract we prove the existence and uniqueness of continuous solutions to the complex monge ampere type equation with the right hand side in l p p 1 on compact hermitian manifolds next we generalise results of eyssidieux guedj and zeriahi 17 18 to compact hermitian manifolds which a priori are not in the fujiki class these generalisations lead to a number of applications we obtain partial results on a conjecture of tosatti and weinkove 40 and on a weak form of a conjecture of demailly and paun 11

estimates for hilbertian koszul homology abstract the objective of this paper is to give new kind of estimates for hilbertian koszul homology inspired by commutative algebra in multivariable fredholm theory

analytic cycles bott chern forms and singular sets for the yang mills flow on kahler manifolds abstract it is shown that the singular set for the yang mills flow on unstable holomorphic vector bundles over compact kahler manifolds is completely determined by the harder narasimhan seshadri filtration of the initial holomorphic bundle we assign a multiplicity to irreducible top dimensional components of the singular set of a holomorphic bundle with a filtration by saturated subsheaves we derive a singular bott chern formula relating the second chern form of a smooth metric on the bundle to the chern current of an admissible metric on the associated graded sheaf this is used to show that the multiplicities of the top dimensional bubbling locus defined via the yang mills density agree with the corresponding multiplicities for the harder narasimhan seshadri filtration the set theoretic equality of singular sets is a consequence

lump type solutions and lump solutions for the 2 1 dimensional generalized bogoyavlensky konopelchenko equation abstract in this paper a 2 1 dimensional generalized bogoyavlensky konopelchenko equation is investigated lump type solutions and lump solutions are obtained with aid of symbolic computation via hirota bilinear method and the ansatz technique by taking the function f in the hirota bilinear form of the 2 1 dimensional generalized bogoyavlensky konopelchenko equation as the general quadratic polynomial function a kind of lump type solution which contains eleven parameters with six arbitrary independent parameters and two non zero conditions is obtained lump solutions are found from the lump type solutions via taking a special set of parameters and the motion track of the lump is also described both theoretically and graphically

families of lagrangian fibrations on hyperkahler manifolds abstract a holomorphic lagrangian fibration on a holomorphically symplectic manifold is a holomorphic map with lagrangian fibers it is known due to huybrechts that a given compact manifold admits only finitely many holomorphic symplectic structures up to deformation we prove that a given compact simple hyperkahler manifold with b 2 7 admits only finitely many deformation types of holomorphic lagrangian fibrations we also prove that all known hyperkahler manifolds are never kobayashi hyperbolic

the lump solutions and the backlund transformation for the three dimensional three wave resonant interaction a backlund transformation is found for the three dimensional three wave resonant interaction and from it n lump exact solutions may be constructed the one lump solution is analyzed in detail and it is shown that it describes such effects as pulse decay upconversion and explosive instabilities all in three dimensions

the fredholm index of a pair of commuting operators ii this paper concerns fredholm theory in several variables and its applications to hilbert spaces of analytic functions one feature is the introduction of ideas from commutative algebra to operator theory specifically we introduce a method to calculate the fredholm index of a pair of commuting operators to achieve this we define and study the hilbert space analogs of samuel multiplicities in commutative algebra then the theory is applied to the symmetric fock space in particular our results imply a satisfactory answer to arveson s program on developing a fredholm theory for pure d contractions when d 2 including both the fredholmness problem and the calculation of indices we also show that arveson s curvature invariant is in fact always equal to the samuel multiplicity for an arbitrary pure d contraction with finite defect rank it follows that the curvature is a similarity invariant

polar and coisotropic actions on kahler manifolds the main result of the paper is that a polar action on a compact irreducible homogeneous kahler manifold is coisotropic this is then used to give new examples of polar actions and to classify coisotropic and polar actions on quadrics

hyperpolygon spaces and moduli spaces of parabolic higgs bundles abstract given an n tuple of positive real numbers we consider the hyperpolygon space x the hyperkahler quotient analogue to the kahler moduli space of polygons in r 3 we prove the existence of an isomorphism between hyperpolygon spaces and moduli spaces of stable rank 2 holomorphically trivial parabolic higgs bundles over c p 1 with fixed determinant and trace free higgs field this isomorphism allows us to prove that hyperpolygon spaces x undergo an elementary transformation in the sense of mukai as crosses a wall in the space of its admissible values we describe the changes in the core of x as a result of this transformation as well as the changes in the nilpotent cone of the corresponding moduli spaces of parabolic higgs bundles moreover we study the intersection rings of the core components of x in particular we find generators of these rings prove a recursion relation in n for their intersection numbers and use it to obtain explicit formulas for the computation of these numbers using our isomorphism we obtain similar formulas for each connected component of the nilpotent cone of the corresponding moduli spaces of parabolic higgs bundles thus determining their intersection rings as a final application of our isomorphism we describe the cohomology ring structure of these moduli spaces of parabolic higgs bundles and of the components of their nilpotent cone

on conservation laws by lie symmetry analysis for 2 1 dimensional bogoyavlensky konopelchenko equation in wave propagation abstract in this paper using the lie group analysis method the infinitesimal generators for 2 1 dimensional bogoyavlensky konopelchenko equation are obtained the new concept of nonlinear self adjointness of differential equations is used for construction of nonlocal conservation laws the conservation laws for the 2 1 dimensional bogoyavlensky konopelchenko equation are obtained by using the new conservation theorem method and the formal lagrangian approach transforming this equation into a system of equations involving with two dependent variables it has been shown that the resultant system of equations is quasi self adjoint and finally the new nonlocal conservation laws are constructed by using the lie symmetry operators

hodge genera of algebraic varieties i the aim of this paper is to study the behavior of hodge theoretic intersection homology genera and their associated characteristic classes under proper morphisms of complex algebraic varieties we obtain formulae that relate parametrized families of global invariants of a complex algebraic variety x to such invariants of singularities of proper algebraic maps defined on x such formulae severely constrain both topologically and analytically the singularities of complex maps even between smooth varieties similar results were announced by the first and third author in 13 32 2007 wiley periodicals inc

interaction solutions for a dimensionally reduced hirota bilinear equation abstract with the help of hirota direct method and symbolic computation two types of interaction solutions to the dimensionally reduced equations in 2 1 dimensions are derived respectively by searching for the solutions to the associated bilinear equations as a combination of positive quadratic function and an exponential hyperbolic cosine function it is interesting that the interaction solutions between lump soliton and one stripe soliton generate the fission and fusion phenomena while the interaction solutions between lump soliton and twin stripe solitons generate the rogue wave

lump solutions to a 2 1 dimensional extended kp equation abstract with the aid of a computer algebra system we present lump solutions to a 2 1 dimensional extended kadomtsev petviashvili equation ekp and give the sufficient and necessary conditions to guarantee analyticity and rational localization of the solutions we plot a few solutions for some specific values of the free parameters involved and finally derive one of the lump solutions of the kadomtsev petviashvili kp equations from the lump solutions of the ekp equation

maximal degree subsheaves of torsion free sheaves on singular projective curves fix integers r k g with r k 0 and g 2 let x be an integral projective curve with g pa x and e a rank r torsion free sheaf on x which is a flat limit of a family of locally free sheaves on x here we prove the existence of a rank k subsheaf a of e such that r deg a k deg e k r k g we show that for every g 9 there is an integral projective curve x x not gorenstein and a rank 2 torsion free sheaf e on x with no rank 1 subsheaf a with 2 deg a deg e g we show the existence of torsion free sheaves on non gorenstein projective curves with other pathological properties

lump solutions of a generalized calogero bogoyavlenskii schiff equation abstract a generalized calogero bogoyavlenskii schiff equation is considered and based on its hirota bilinear form a class of lump solutions is explicitly generated via symbolic computations with maple together with plots of a specific lump solution the result enlarges the category of nonlinear partial differential equations which possess lump solutions

lump solutions to the kadomtsev petviashvili i equation with a self consistent source abstract based on symbolic computations lump solutions to the kadomtsev petviashvili i kpi equation with a self consistent source kpiescs are constructed by using the hirota bilinear method and an ansatz technique in contrast with lower order lump solutions of the kadomtsev petviashvili kp equation the presented lump solutions to the kpiescs exhibit more diverse nonlinear phenomena the method used here is more natural and simpler

algebraic deformations of compact kahler surfaces ii in the first version of this paper a short proof was given of kodaira s result that every compact kahler surface is a deformation of an algebraic surface under the extra assumption that the infinitesimal deformations of the surface were unobstructed in this paper the extra assumption is removed

diversity of interaction solutions to the 2 1 dimensional ito equation abstract we aim to show the diversity of interaction solutions to the 2 1 dimensional ito equation based on its hirota bilinear form the proof is given through maple symbolic computations an interesting characteristic in the resulting interaction solutions is the involvement of an arbitrary function special cases lead to lump solutions lump soliton solutions and lump kink solutions two illustrative examples of the resulting solutions are displayed by three dimensional plots and contour plots