相关论文: Derived categories of generalized Kummer varieties…

We study relatively semi-stable vector bundles and their moduli on non-K\"ahler principal elliptic bundles over compact complex manifolds of arbitrary dimension. The main technical tools used are the twisted Fourier-Mukai transform and a…

This paper is a sequel to math.AG/0203287. A generalization of the Mukai flop has been studied by E. Markman. Here we call it a stratified Mukai flop. In this paper, we observe that, for a stratified Mukai flop: $X \to \bar{X} \leftarrow…

We show that for many moduli spaces M of torsion sheaves on K3 surfaces S, the functor D(S) -> D(M) induced by the universal sheaf is a P-functor, hence can be used to construct an autoequivalence of D(M), and that this autoequivalence can…

We prove a version of the Kawamata-Morrison ample cone conjecture for projective irreducible holomorphic symplectic manifolds deformation equivalent to either the Hilbert scheme of n points on a K3 surface, or a generalized Kummer variety.

We use twisted Fourier-Mukai transforms to study the relation between an abelian fibration on a holomorphic symplectic manifold and its dual fibration. Our reasoning leads to an equivalence between the derived category of coherent sheaves…

We study quantum geometry of Nakajima quiver varieties of two different types - framed A-type quivers and ADHM quivers. While these spaces look completely different we find a surprising connection between equivariant K-theories thereof with…

We give a proof of Mukai's Theorem on the existence of certain exceptional vector bundles on prime Fano threefolds. To our knowledge this is the first complete proof in the literature. The result is essential for Mukai's biregular…

We introduce a double framing construction for moduli spaces of quiver representations. It allows us to reduce certain sheaf cohomology computations involving the universal representation, to computations involving line bundles, making them…

We study the Kodaira dimension of moduli spaces of polarized hyperk\"ahler varieties deformation equivalent to the Hilbert scheme of points on a K3 surface or to O'Grady's ten dimensional variety. This question was studied by…

In general, if M is a moduli space of stable sheaves on X, there is a unique alpha in the Brauer group of M such that a pi_M^* alpha^{-1}-twisted universal sheaf exists on X times M. In this paper we study the situation when X and M are K3…

In this article, we study the $G$-autoequivalences of the derived category $\mathbf{D}^b_G(A)$ of $G$-equivariant objects for an abelian variety $A$ with $G$ being a finite subgroup of $\mathrm{Pic}^0(A)$. We provide a result analogue to…

In this note, we shall prove that two smooth projective varieties of dim 2n connected by a Mukai flop have equivalent bounded derived categories. More precisely, let $\phi : X - - \to X^+$ be a Mukai flop with centers $Y \subset X$ and $Y^+…

I employ methods from derived algebraic geometry to give a uniform moduli-theoretic construction of special cycle classes on integral models many Shimura varieties of Hodge type, including unitary, quaternionic, and orthogonal Shimura…

We study the relationship between derived categories of factorizations on gauged Landau-Ginzburg models related by variations of the linearization in Geometric Invariant Theory. Under assumptions on the variation, we show the derived…

We prove that if two very general cubic fourfolds are L-equivalent then they are isomorphic, and we observe that there exist special cubic fourfolds which are L-equivalent but not isomorphic. When the cubic fourfolds are very general in…

Let X be an abelian scheme over a scheme B. The Fourier--Mukai transform gives an equivalence between the derived category of X and the derived category of the dual abelian scheme. We partially extend this to certain schemes X over B (which…

We study the Hodge theory of twisted derived categories and its relation to the period-index problem. Our main contribution is the development of a theory of twisted Mukai structures for topologically trivial Brauer classes on arbitrary…

This paper is concerned with non-symplectic involutions of irreducible symplectic manifolds of $K3^{[n]}$-type. We will give a criterion for deformation equivalence and use this to give a lattice-theoretic description of all deformation…

We lift to equivariant algebra three closely related classical algebraic concepts: abelian group objects in augmented commutative algebras, derivations, and K\"ahler differentials. We define Mackey functor objects in the category of Tambara…

We propose two conjectures on a moduli theoretic approach to constructing Lagrangian subvarieties of hyperk\"ahler varieties arising from the Kuznetsov components of cubic fourfolds or Gushel--Mukai fourfolds. Then we verify the conjectures…