Autoequivalences of Derived Category of A K3 Surface and Monodromy Transformations

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We consider autoequivalences of the bounded derived category of coherent sheaves on a K3 surface. We prove that the image of the autoequivalences has index at most two in the group of the Hodge isometries of the Mukai lattice. Motivated by homological mirror symmetry we also consider the mirror counterpart, i.e. symplectic version of it. In the case of $ρ(X)=1$, we find an explicit formula which reproduces the number of Fourier-Mukai (FM) partners from the monodromy problem of the mirror K3 family. We present an explicit example in which a monodromy action does not come from an autoequivalence of the mirror side.
AMSTeX, 27 pages, 2 figures; reference added, and minor corrections made

Keywords

Algebraic Geometry, High Energy Physics - Theory, Symplectic Geometry, 14J28

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/63056

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0201047
 http://arxiv.org/abs/math/0201047

Collections

arXiv