Related papers: Regularity on abelian varieties I

We compute moduli spaces of Bridgeland stable objects on an irreducible principally polarized complex abelian surface corresponding to twisted ideal sheaves. We use Fourier-Mukai techniques to extend the ideas of Arcara and Bertram to…

We partially generalize the theory of semihomogeneous bundles on an abelian variety $A$ developed by Mukai. This involves considering abelian subvarieties $Y\subset X_A=A\times\hat{A}$ and studying coherent sheaves on $A$ invariant under…

Let C be small category and A an arbitrary category. Consider the category C(A) whose objects are functors from C to A, and whose morphisms are natural transformations. Given a functor F : A --> B one obtains an induced functor F_C : C(A)…

We study the Fourier-Mukai transform for holonomic D-modules on complex abelian varieties. Among other things, we show that the cohomology support loci of a holonomic D-module are finite unions of linear subvarieties, which go through…

We develop some methods for studying the Fourier-Mukai partners of an algebraic variety. As applications we prove that abelian varieties have finitely many Fourier-Mukai partners and that they are uniquely determined by their derived…

This paper deals with properties of filtrations on vector spaces indexed by partially ordered finitely generated abelian groups, which we call multifiltrations. We discuss the usual properties of filtrations, like exhaustivity and…

We will discuss the Fourier-Mukai partners of a given abelian variety. The first part of the note is to give some basic theory of Fourier-Mukai partners and semi-homogenous vector bundles, then we will discuss the case when the kernel of an…

Bridgeland stability condition is preserved under the Fourier-Mukai transform by its definition. We explain the relation with Gieseker stability. By studying the wall-crossing behavior, we reprove that the moduli spaces of stable sheaves on…

We give an introductory review of Fourier-Mukai transforms and their application to various aspects of moduli problems, string theory and mirror symmetry. We develop the necessary mathematical background for Fourier-Mukai transforms such as…

We establish a, and conjecture further, relationship between the existence of subvarieties representing minimal cohomology classes on principally polarized abelian varieties, and the generic vanishing of certain sheaf cohomology. The main…

We describe the birational correspondences, induced by the Fourier-Mukai functor, between moduli spaces of semistable sheaves on elliptic surfaces with sections, using the notion of $P$-stability in the derived category. We give explicit…

For a Fourier-Mukai transform whose kernel is the Poincare line bundle, we study the preservation of Gieseker stability of sheaves on any abelian surface.

Results on stability of tautological sheaves on Hilbert schemes of points are extended to higher dimensions and transferred to abelian surfaces and to the restriction of tautological sheaves to generalised Kummer varieties. This provides a…

We prove that any proper Fourier-Mukai partner of an abelian variety is again an abelian variety, by analyzing the Matsui spectrum of the derived category. This result was previously obtained by Huybrechts and Nieper-Wisskirchen in the case…

We consider a relative Fourier-Mukai transform defined on elliptic fibrations over an arbitrary normal base scheme. This is used to construct relative Atiyah sheaves and generalize Atiyah's and Tu's results about semistable sheaves over…

Let $A$ be an abelian variety over a field. The homogeneous (or translation-invariant) vector bundles over $A$ form an abelian category ${\rm HVec}_A$; the Fourier-Mukai transform yields an equivalence of ${\rm HVec}_A$ with the category of…

We introduce the notion of (twisted) quiver representations in abelian categories and study the category of such representations. We construct standard resolutions and coresolutions of quiver representations and study basic homological…

The geometric and algebraic properties of smooth projective varieties with 1-regular structure sheaf are well understood, and the complete classification of these varieties is a classical result. The aim of this paper is to study the next…

We study the property of \emph{continuous Castelnuovo-Mumford regularity}, for semihomogeneous vector bundles over a given Abelian variety, which was formulated in \cite{Kuronya:Mustopa:2020} by K\"{u}ronya and Mustopa. Our main result…

We shall introduce a stability condition for a coherent sheaf associated to an elliptic surface. Then we study the behavior under relative Fourier-Mukai transforms.