Autoequivalences of Derived Category of A K3 Surface and Monodromy Transformations
Algebraic Geometry
2007-05-23 v3 High Energy Physics - Theory
Symplectic Geometry
Abstract
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 , 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.
Keywords
Cite
@article{arxiv.math/0201047,
title = {Autoequivalences of Derived Category of A K3 Surface and Monodromy Transformations},
author = {Shinobu Hosono and Bong H. Lian and Keiji Oguiso and Shing-Tung Yau},
journal= {arXiv preprint arXiv:math/0201047},
year = {2007}
}
Comments
AMSTeX, 27 pages, 2 figures; reference added, and minor corrections made