相关论文: Symplectic biextensions and a generalization of th…

We survey and investigate some computational aspects of the Fourier-Mukai transform.

We systematically develop a transform of the Fourier-Mukai type for sheaves on symplectic manifolds $X$ of any dimension fibred in Lagrangian tori. One obtains a bijective correspondence between unitary local systems supported on Lagrangian…

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…

Let $G$ be a compact, connected, simply-connected Lie group. We use the Fourier-Mukai transform in twisted $K$-theory to give a new proof of the ring structure of the $K$-theory of $G$.

We propose a slightly modified definition for the Fourier-Mukai transform (on abelian varieties) that makes it much easier to remember various formulas. As an application, we give relatively short proofs for two important theorems: the…

We study deformations of Fourier-Mukai transforms in general complex analytic settings. We start with two complex manifolds X and Y together with a coherent Fourier-Mukai kernel P on their product. Suppose that P implements an equivalence…

We provide an analog of the Hilbert-Chow morphism for generalized discriminants.

In complex K-theory, the Fourier-Mukai transform is an isomorphism between K-theory groups of a torus and its dual torus which is defined by pullback, tensoring by the Poincar\'e line bundle and pushforward. The Fourier-Mukai transform…

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…

In this expository paper, we discuss how Fourier-Mukai-type transformations, which we call SYZ mirror transformations, can be applied to provide a geometric understanding of the mirror symmetry phenomena for semi-flat Calabi-Yau manifolds…

We define a Fourier transform and a convolution product for functions and distributions on Heisenberg--Clifford Lie supergroups. The Fourier transform exchanges the convolution and a pointwise product, and is an intertwining operator for…

We apply the methods of C{\u{a}}ld{\u{a}}raru to construct a twisted Fourier-Mukai transform between a pair of holomorphic symplectic four-folds. More precisely, we obtain an equivalence between the derived category of coherent sheaves on a…

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 prove the crepant transformation conjecture for relative Grassmann flops over a smooth base $B$. We show that the $I$-functions of the respective GIT quotients are related by analytic continuation and a symplectic transformation. We…

There is a beautiful correspondence between configurations of lines on a rational surface and tautological bundles over that surface. We extend this correspondence to families, by means of a generalized Fourier-Mukai transform that relates…

We study Fourier-Mukai transforms for smooth projective varieties whose canonical bundles have finite order, and relate them to equivariant transforms on certain finite covering spaces. Our results lead to new equivalences of derived…

Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…

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…

A new approach to the quantization of constrained or otherwise reduced classical mechanical systems is proposed. On the classical side, the generalized symplectic reduction procedure of Mikami and Weinstein, as further extended by Xu in…

We interpret symplectic geometry as certain sheaf theory by constructing a sheaf of curved A_\infty algebras which in some sense plays the role of a "structure sheaf" for symplectic manifolds. An interesting feature of this "structure…