Related papers: The intersection complex as a weight truncation an…
Homotopy continuation provides a numerical tool for computing the equivalence of a smooth variety in an intersection product. Intersection theory provides a theoretical tool for relating the equivalence of a smooth variety in an…
We introduce trim resolutions of complex algebraic varieties, a strengthening of the notion of small resolution. We prove that the characteristic cycle of the intersection cohomology sheaf of a variety admitting a trim resolution is…
We realize certain graded Nakajima varieties of finite Dynkin type as orbit closures of repetitive algebras of Dynkin quivers. As an application, we obtain that the perverse sheaves introduced by Nakajima for describing irreducible…
We prove that the derived direct image of the constant sheaf with field coefficients under any proper map with smooth source contains a canonical summand. This summand, which we call the geometric extension, only depends on the generic…
We determine the structure of the intersection of a finitely generated subgroup of a semiabelian variety $G$ defined over a finite field with a closed subvariety $X\subset G$.
In [5] the structure of the bifurcation diagrams of a class of superlinear indefinite problems with a symmetric weight was ascertained, showing that they consist of a primary branch and secondary loops bifurcating from it. In [4] it has…
Cohomology of the variational bicomplex in the calculus of variations in classical field theory are computed in the class of exteriror forms of finite jet order. This provides a solution of the global inverse problem of the finite order…
The Hurwitz form of a projective variety characterizes linear spaces of complementary dimension which meet the variety non-transversally. We extend this notion to varieties in a product of projective spaces. This parallels the multigraded…
We define and describe the properties of a class of perverse sheaves which is very useful when the base ring is not a field.
The goal of this survey is to describe some recent results concerning the L 2 extension of holomorphic sections or cohomology classes with values in vector bundles satisfying weak semi-positivity properties. The results presented here are…
Let X be a smooth, connected, closed subvariety of a complex vector space V. The asymptotic cone as(X) is naturally equipped with a nearby cycles sheaf P coming from the specialization of X to as(X). We show that if X is transverse to…
In this paper, we provide a relative hypercohomology version of Serre's GAGA theorem. We prove that the relative hypercohomology of a complex of sheaves on a complex projective variety is isomorphic to the relative hypercohomology of its…
We present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field representation. More precisely, we show that…
Under simplifying hypotheses we prove a relation between the l-adic cohomology of the basic stratum of a Shimura variety of PEL-type modulo a prime of good reduction of the reflex field and the cohomology of the complex Shimura variety. In…
We determine versal non-commutative deformations of some simple collections in the categories of perverse coherent sheaves arising from tilting generators for projective morphisms.
In this paper, we prove the Shafarevich conjecture for certain complete intersections of hypersurfaces in abelian varieties defined over a number field $K$ using the Lawrence-Venkatesh method. The main new inputs we need are computation of…
For an acyclic quiver with three vertices, we consider the canonical decomposition of a non-Schurian root and associate certain representations of a generalized Kronecker quiver. These representations correspond to points contained in the…
The purpose of this note is to show that the subvarieties of small degree inside a general hypersurface of large degree come from intersecting with linear spaces or other varieties.
The task of this survey is to present various results on intersection patterns of convex sets. One of main tools for studying intersection patterns is a point of view via simplicial complexes. We recall the definitions of so called…
We study a general method of the field intersection problem of generic polynomials over an arbitrary field $k$ via formal Tschirnhausen transformation. In the case of solvable quintic, we give an explicit answer to the problem by using…