Related papers: Characteristic varieties and constructible sheaves

We discuss derived categories of coherent sheaves on algebraic varieties. We focus on the case of non-singular Calabi-Yau varieties and consider two unsolved problems: proving that birational varieties have equivalent derived categories,…

We investigate the bounded derived category of coherent sheaves on irreducible singular projective curves of arithmetic genus one. A description of the group of exact auto-equivalences and the set of all t-structures of this category is…

We give a complete classification of semistable rank two sheaves on three-dimensional projective space with maximal third Chern character. This implies an explicit description of their moduli spaces. As an open subset they contain rank two…

We study the compatibility with proper push-forward of the characteristic cycles of a constructible complex on a smooth variety over a perfect field.

We discuss relations between the motives of two varieties with equivalent derived categories of coherent sheaves.

We classify Chern characters of semistable sheaves up to rank four in three dimensional projective space. As a corollary we show that moduli spaces of semistable sheaves between rank zero and four with maximal third Chern character are…

We classify the unipotent character sheaves on a fixed connected component of a reductive algebraic group under a mild hypothesis on the characteristic of the ground field.

We construct rational elliptic surfaces of index two by explicitly constructing their associated Halphen pencils in the projective plane $\mathbb{P}^2$. For each of the types of singular fibers that occur we construct at least one example…

In the framework of Abstract Differential Geometry, we show that to a given principal sheaf and a representation of its stuctural sheaf in $A^n$, where A is a sheaf of associative, commutative, unital algebras (over R or C), we associate a…

We consider a relation between local and global characteristics of a differential algebraic variety. We prove that dimension of tangent space for every regular point of an irreducible differential algebraic variety coincides with dimension…

Let A be a character sheaf on a reductive connected group G over an algebraically closed field. Assuming that the characteristic is not bad, we show that for certain conjugacy classes D in G the restriction of A to D is a local system up to…

We study linear pencils of curves on normal surface singularities. Using the minimal good resolution of the pencil, we describe the topological type of generic elements of the pencil and characterize the behaviour of special elements. Then…

There is an interplay between models, specified by variables and equations, and their connections to one another. This dichotomy should be reflected in the abstract as well. Without referring to the models directly -- only that a model…

Let $X$ be a smooth projective variety. We study admissible subcategories of the bounded derived category of coherent sheaves on $X$ whose support is a proper subvariety $Z \subset X$. We show that any one-dimensional irreducible component…

We construct local models of Shimura varieties and investigate their singularities, with special emphasis on wildly ramified cases. More precisely, with the exception of odd unitary groups in residue characteristic $2$ we construct local…

In this article we formulate and prove the main theorems of the theory of character sheaves on unipotent groups over an algebraically closed field of characteristic p>0. In particular, we show that every admissible pair for such a group G…

Let G be a reductive groups over an algebraically closed field k. Let P^{(i)} be associated parabolic subgroups, and X^{(i)}:=T^*G/P^i. The bounded derived categories of coherent sheaves on X^{(i)} are equivalent, but there is no canonical…

Let $C$ be an irreducible projective plane curve in the complex projective space ${\mathbb{P}}^2$. The classification of such curves, up to the action of the automorphism group $PGL(3,{\mathbb{C}})$ on ${\mathbb{P}}^2$, is a very difficult…

We introduce in this paper a hypercohomology version of the resonance varieties and obtain some relations to the characteristic varieties of rank one local systems on a smooth quasi-projective complex variety $M$, see Theorem (3.1) and…

For a smooth morphism $f: X \longrightarrow \Sigma$ of real analytic manifolds and an $\mathbb{R}$-constructible sheaf $F$ on $X$ satisfying some condition, we define a family of Lagrangian cycles parameterized by $\Sigma$ that we call the…