Related papers: The Fourier-Mukai transform made easy

Let X be a smooth elliptic fibration over a smooth base B. Under mild assumptions, we establish a Fourier-Mukai equivalence between the derived categories of two objects, each of which is an O^* gerbe over a genus one fibration which is a…

We construct a version of Fourier transform for families of real tori. This transform defines a functor from certain category associated with a symplectic family of tori to the category of holomorphic vector bundles on the dual family (the…

These are notes of a talk based on the work arXiv:1212.3630 joint with A. Aizenbud. Let V be a finite-dimensional vector space over a local field F of characteristic 0. Let f be a function on V of the form $f(x)= \psi (P(x))$, where P is a…

For a given Fourier-Mukai equivalence of bounded derived categories of coherent sheaves on smooth quasi-projective varieties, we construct Fourier-Mukai equivalences of derived factorization categories of gauged Landau-Ginzburg (LG) models.…

Given a polarized tropical affine torus, we show that the fibered Lagrangian cobordism group of the corresponding symplectic manifold admits a natural geometric filtration of finite length. This contrasts with results of Sheridan-Smith in…

We prove a certain uniform version of the Shafarevich Conjecture. As a corollary, we prove the Rasmussen-Tamagawa Conjecture for a particular class of abelian varieties $A$ defined over a number $K$ of dimension $g$ having everywhere…

Given two compact hyperk\"ahler surfaces $X$ and $Y$ and a holomorphic vector bundle $Q$ on $X\times Y$, which is a generalized instanton, one can define a Fourier-Mukai transform, which, under suitable assumptions, maps vector bundles on…

In most cases where it had been shown to exist the derived McKay correspondence D(Y) --> D^G(C^n) can be written as a Fourier-Mukai transform which sends point sheaves of the crepant resolution Y to pure sheaves in D^G(C^n). We give a…

Let f:C -> A be an entire holomorphic curve into a semi-Abelian variety A. Then the Zariski closure of f(C) is a translate of a semi-Abelian subvariety of A (logarithmic Bloch-Ochiai's theorem). The purpose of the present paper is to…

We show that the conjectural construction proposed by Bayer, Bertram, Macr\'i and Toda gives rise to Bridgeland stability conditions for a principally polarized abelian three-fold with Picard rank one by proving that tilt stable objects…

Let $X$ be an irreducible algebraic variety over $\mathbb{C}$, endowed with an algebraic foliation ${\cal{F}}$. In this paper, we introduce the notion of minimal invariant variety $V({\cal{F}},Y)$ with respect to $({\cal{F}},Y)$, where $Y$…

We propose two new approaches to the Tannakian Galois groups of holonomic D-modules on abelian varieties. The first is an interpretation in terms of principal bundles given by the Fourier-Mukai transform, which shows that they are almost…

We show that the hypercohomology of most character twists of perverse sheaves on a complex abelian variety vanishes in all non-zero degrees. As a consequence we obtain a vanishing theorem for constructible sheaves and a relative vanishing…

Let $f \colon X \to A$ be a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). We show that the sheaves $f_* \omega_X^{\otimes m}$ become globally generated after pullback by an isogeny. We…

We give a condition for an exact functor between triangulated categories to be an equivalence. Applications to Fourier-Mukai transforms are discussed. In particular, we obtain a large number of such transforms for K3 surfaces.

We define a Fourier-Mukai transform for Higgs bundles on smooth curves and study its properties. It is shown that the transform of a stable zero-degree Higgs bundle is an algebraic vector bundle on the cotangent bundle of the Jacobian of…

We prove that a large class of natural transformations (consisting roughly of those constructed via composition from the "functorial" or "base change" transformations) between two functors of the form $\cdots f^* g_* \cdots$ actually has…

Assuming the standard framework of mirror symmetry, a conjecture is formulated describing how the diffeomorphism group of a Calabi-Yau manifold Y should act by families of Fourier-Mukai transforms over the complex moduli space of the mirror…

In this note, we prove a generalization of Efimov's computation for the universal localizing invariant of categories of sheaves with certain microsupport constraints. The proof is based on certain categorical equivalences given by the…

On the product elliptic threefold $X = C \times S$ where $C$ is an elliptic curve and $S$ is a K3 surface of Picard rank 1, we define a notion of limit tilt stability, which satisfies the Harder-Narasimhan property. We show that under the…