birational automorphism groups and the movable cone theorem for calabi yau manifolds of wehler type via universal coxeter groups thanks to the theory of coxeter groups we produce the first family of calabi yau manifolds x of arbitrary dimension n for which rm bir x is infinite and the kawamata morrison movable cone conjecture is satisfied for this family the movable cone is explicitly described it s fractal nature is related to limit sets of kleinian groups and to the apollonian gasket then we produce explicit examples of biregular automorphisms with positive entropy on some calabi yau varieties

geometric reid s recipe for dimer models crepant resolutions of three dimensional toric gorenstein singularities are derived equivalent to noncommutative algebras arising from consistent dimer models by choosing a special stability parameter and hence a distinguished crepant resolution y this derived equivalence generalises the fourier mukai transform relating the g hilbert scheme and the skew group algebra mathbb c x y z g for a finite abelian subgroup of mathrm sl 3 mathbb c we show that this equivalence sends the vertex simples to pure sheaves except for the zero vertex which is mapped to the dualising complex of the compact exceptional locus this generalises results of cautis logvinenko j reine angew math 636 193 236 2009 and cautis craw logvinenko j reine angew math arxiv 1205 3110 2014 to the dimer setting though our approach is different in each case we also describe some of these pure sheaves explicitly and compute the support of the remainder providing a dimer model analogue of results from logvinenko j algebra 324 2064 2087 2010

boundary controllability of sobolev type abstract nonlinear integrodifferential systems sufficient conditions are established for boundary controllability of various classes of sobolev type nonlinear systems including integrodifferential systems in banach spaces the results are obtained using the strongly continuous semigroup of operators and the banach contraction principle examples are provided to illustrate the theory

flops of g hilb and equivalences of derived categories by variation of git quotient for a finite subgroup g in sl 3 c bridgeland king and reid proved that the moduli space of g clusters is a crepant resolution of the quotient c 3 g this paper considers the moduli spaces m theta introduced by kronheimer and further studied by sardo infirri which coincide with g hilb for a particular choice of the git parameter theta for g abelian we prove that every projective crepant resolution of c 3 g is isomorphic to m theta for some parameter theta the key step is the description of git chambers in terms of the k theory of the moduli space via the appropriate fourier mukai transform we also uncover explicit equivalences between the derived categories of moduli m theta for parameters lying in adjacent git chambers

boundary controllability of differential equations with nonlocal condition for a semilinear boundary control system with a nonlocal condition using a banach fixed point theorem we prove the boundary controllable and we give an application

existence and controllability results for impulsive partial functional differential inclusions abstract in this paper we prove the existence and the controllability of mild and extremal mild solutions for first order semilinear densely defined impulsive functional differential inclusions in separable banach spaces with local and nonlocal conditions

global existence for semilinear evolution equations with nonlocal conditions abstract in this paper we study the global existence of solutions for semilinear evolution equations with nonlocal conditions via a fixed point analysis approach using the leray schauder alternative we derive conditions under which a solution exists globally

artin group actions on derived categories of threefolds motivated by the enhanced gauge symmetry phenomenon of the physics literature and mirror symmetry this paper constructs an action of an artin group on the derived category of coherent sheaves of a smooth quasiprojective threefold containing a configuration of ruled surfaces described by a finite type dynkin diagram the action ex tends over deformations of the threefold via a compatible action of the corresponding re flection group on the base of its deformation space all finite type dynkin diagrams are realized

existence results and asymptotic behavior for nonlocal abstract cauchy problems the purpose of this paper is to study the existence and asymptotic behavior of solutions for cauchy problems with nonlocal initial datum generated by accretive operators in banach spaces

periodic solutions for some nonautonomous semilinear boundary evolution equations abstract in this work we study the massera problem for the existence of a periodic mild solution of a class of nonautonomous semilinear boundary evolution equations 0 1 x t a m t x t f t x t t 0 l t x t t x t g t x t t 0 x 0 x 0 first we prove the existence of a periodic solution for nonhomogeneous boundary evolution equations under the existence of a bounded solution on the right half real line next by using a fixed point theorem we investigate the existence of periodic solutions in the semilinear case we end with an application to a periodic heat equation with semilinear boundary conditions

the cone conjecture for calabi yau pairs in dimension 2 a central idea of minimal model theory as formulated by mori is to study algebraic varieties using convex geometry the cone of curves of a projective variety is defined as the convex cone spanned by the numerical equivalence classes of algebraic curves the dual cone is the cone of nef line bundles for fano varieties varieties with ample anticanonical bundle these cones are rational polyhedral by the cone theorem 21 theorem 3 7 for more general varieties these cones are not well understood they can have infinitely many isolated extremal rays or they can be round both phenomena occur among calabi yau varieties such as k3 surfaces 22 which can be considered the next simplest varieties after fano varieties the morrison kawamata cone conjecture would give a clear picture of the nef cone for calabi yau varieties 29 30 19 the conjecture says that the action of the automorphism group of the variety on the nef cone has a rational polyhedral fundamental domain the conjecture includes an analogous statement about the movable cone see section 2 for details thus for calabi yau varieties the failure of the nef cone to be rational polyhedral is always explained by an infinite discrete group of automorphisms of the variety it is not clear where these automorphisms should come from nonetheless the conjecture has been proved for calabi yau surfaces by sterk looijenga and namikawa 41 33 19 the heart of the proof being the torelli theorem for k3 surfaces of piatetski shapiro and shafarevich 3 theorem 11 1 kawamata proved the cone conjecture for all 3 dimensional calabi yau fiber spaces over a positive dimensional base 19 the conjecture is wide open for calabiyau 3 folds despite significant results by oguiso and peternell 38 szendroi 43 uehara 46 and wilson 48 the conjecture was generalized from calabi yau varieties to klt calabi yau pairs x in 45 here is a divisor on x and calabi yau means that kx rather than kx is numerically trivial in this paper we prove the cone conjecture for all klt calabi yau pairs of dimension 2 theorem 4 1 using the geometry of groups acting on convex cones and reduction to the case of k3 surfaces this is enough to show that the conjecture is reasonable in the greater generality of pairs more concretely the theorem gives control over the nef cone and the automorphism group for a large class of rational surfaces including the fano surfaces as well as many others in particular we get a good description of when the cox ring or total coordinate ring is finitely generated in this class of surfaces corollary 5 1 thanks to caucher birkar igor dolgachev brian harbourne artie prendergastsmith chenyang xu and the referees for their comments

existence and controllability results for nondensely defined impulsive semilinear functional differential inclusions abstract in this paper we shall establish sufficient conditions for the existence of integral solutions and extremal integral solutions for some nondensely defined impulsive semilinear functional differential inclusions in separable banach spaces we shall rely on a fixed point theorem for the sum of completely continuous and contraction operators the question of controllability of these equations and the topological structure of the solutions set are considered too

the weil petersson geometry of the moduli space of su n 3 calabi yau manifolds i the weil petersson metric is defined on the moduli space of calabi yau manifolds the curvature of this weil petersson metrics is computed and its potential is explicitely defined it is proved that the moduli space of calabi yau manifolds is unobstructed see tian

the tangent bundle of a calabi yau manifold deformations and restriction to rational curves the tangent bundle x of a calabi yau threefoldx is the only known example of a stable bundle with non trivial restriction to any rational curve onx by deforming the direct sum of x and the trivial line bundle one can try to obtain new examples we use algebro geometric techniques to derive results in this direction the relation to the finiteness of rational curves on calabi yau threefolds is discussed

controllability of semilinear boundary problems with nonlocal initial conditions the main purpose of this paper is the existence of solutions and controllability for semilinear boundary problems with nonlocal initial conditions we show that the solutions are given by a variation of constants formula which allows us to study the exact controllability for this kind of problems with control and nonlinear terms at the boundary the included application to a size structured population equation provides a motivation for abstract results

deformation theory of singular symplectic n folds by a symplectic manifold or a symplectic n fold we mean a compact kaehler manifold of even dimension n with a non degenerate holomorphic 2form i e is a nowhere vanishing n form this notion is generalized to a variety with singularities we call x a projective symplectic variety if x is a normal projective variety with rational gorenstein singularities and if the regular locus u of x admits a non degenerate holomorphic 2 form a symplectic variety will play an important role together with a singular calabi yau variety in the generalized bogomolov decomposition conjecture now that essentially a few examples of symplectic manifolds are discovered it seems an important task to seek new symplectic manifolds by deforming symplectic varieties in this paper we shall study a projective symplectic variety from a view point of deformation theory if x has a resolution x x such that x is a symplectic manifold we say that x has a symplectic resolution our first results are concerned with a birational contraction map of a symplectic manifold

controllability of evolution differential inclusions in banach spaces abstract in this paper we consider the controllability of a certain class of evolution differential inclusions in banach spaces a sufficient condition is established by using a recent fixed point theorem for multi valued maps due to dhage combined with an evolution system an example is also given to illustrate our result

grothendieck groups of quotient singularities given a quotient singularity r s g where s c x 1 x n is the formal power series ring in n variables over the complex numbers c there is an epimorphism of grothendieck groups g 0 s g g 0 r where s g is the skew group ring and w is induced by the fixed point functor the grothendieck group of s g carries a natural structure of a ring isomorphic to g 0 c g we show how the structure of g 0 r is related to the structure of the ramification locus of v over v g and the action of g on it

constraining the kahler moduli in the heterotic standard model phenomenological implications of the volume of the calabi yau threefolds on the hidden and observable m theory boundaries together with slope stability of their corresponding vector bundles constrain the set of kahler moduli which give rise to realistic compactifications of the strongly coupled heterotic string when vector bundles are constructed using extensions we provide simple rules to determine lower and upper bounds to the region of the kahler moduli space where such compactifications can exist we show how small these regions can be working out in full detail the case of the recently proposed heterotic standard model more explicitly we exhibit kahler classes in these regions for which the visible vector bundle is stable on the other hand there is no polarization for which the hidden bundle is stable

controllability of evolution inclusions with nonlocal conditions in this paper we examine controllability problems of evolution inclusions with nonlocal conditions using kakutani s fixed point theorem and schauder s fixed point theorem we establish sufficient conditions for the controllability under convex and nonconvex orientor fields respectively

controllability of sobolev type integrodifferential systems in banach spaces sufficient conditions for controllability of sobolev type integrodifferential systems in banach spaces are established the results are obtained using compact semigroups and the schauder fixed point theorem as an example is provided to illustrate the results

k theory of endomorphism rings and of rings of invariants abstract this paper gives the following description ofk0of the endomorphism ring of a finitely generated projective module t heorem let t be a ring and p a finitely generated projective t module let i be the trace ideal of p then k0 end pt is isomorphic to a subgroup of k0 t i if further the natural map k1 t k1 t i is surjective then k0 end pt is isomorphic to the subgroup of k0 t generated by the direct summands of pn for n n as a corollary we can determinek0of the ring of invariants for many free linear actions in particular the following result is proved t heorem let v be a fixed point free linear representation of a finite group g over a field k of characteristic zero and let s v be the symmetric algebra of v let k be any finite dimensional k vector space then k0 s v g ks k s v g ks k similar results are given for suitable noncommutative versions ofs v

on 2 4 complete intersection threefolds that contain an enriques surface we study nodal complete intersection threefolds of type 2 4 in mathbb p 5 which contain an enriques surface in its fano embedding we completely determine calabi yau birational models of a generic such threefold these models have hodge numbers h 11 2 h 12 32 we also describe calabi yau varieties with hodge numbers h 11 h 12 equal to 2 26 23 5 and 31 1 the last two pairs of hodge numbers are to the best of our knowledge new

sectional curvatures of kahler moduli if x is a compact kahler manifold of dimension n we let open image in new window denote the cone of kahler classes and open image in new window the level set given by classes d with d n 1 this space is naturally a riemannian manifold and is isometric to the manifold open image in new window of kahler forms with n some fixed volume form equipped with the hodge metric as studied previously by huybrechts we study these spaces further in particular their geodesics and sectional curvatures conjecturally at least for calabi yau manifolds and probably rather more generally these sectional curvatures should be bounded between open image in new window and zero we find simple formulae for the sectional curvatures and prove both the bounds hold for various classes of varieties developing along the way a mirror to the weil petersson theory of complex moduli in the case of threefolds with h1 1 3 we produce an explicit formula for this curvature in terms of the invariants of the cubic form this enables us to check the bounds by computer for a wide range of examples finally we explore the implications of the non positivity of these curvatures

existence of mild solutions for fractional integrodifferential equations of sobolev type with nonlocal conditions abstract this paper is concerned with the fractional integrodifferential equations of sobolev type with nonlocal condition in a separable banach space with the help of the theory of propagation family as well as the theory of the measures of noncompactness and the condensing maps we obtain the existence result of mild solutions for above equations two examples are given to illustrate the existence theorem

grothendieck groups of invariant rings filtrations we investigate the grothendieck group ga r of finitely generated modules over the ring of invariants r s g of the action of a finite group g on an fbn ring s under the assumption that the trace map from s to r is surjective using a certain filtration of g0 r that is defined in terms of gabriel rentschler krull dimension properties of g0 r are derived to a large extent from the connections between the sets of prime ideals of 5 and r a crucial ingredient is an equivalence relation on spec that was introduced by montgomery 25 for example we show that rank go rank g0 s g q 1 a where q runs over the equivalence classes in spec r and c denotes g coinvariants the torsion subgroup of g0 r is also considered we apply our results to group actions on the weyl algebra in positive characteristics the quantum plane and the localized quantum plane for roots of unity

boundary control problems with nonlinear state equation first order necessary conditions of optimality are obtained for boundary control problems governed by parabolic equations with nonlinear boundary value conditions

nonlocal cauchy problems for neutral functional differential and integrodifferential inclusions in banach spaces in this paper we investigate the existence of mild solutions on a compact interval to initial value problems for neutral functional differential and integrodifferential inclusions in banach spaces with nonlocal conditions the results are obtained by using a fixed point theorem for condensing maps due to martelli