Derived categories of irreducible projective curves of arithmetic genus one
Algebraic Geometry
2007-05-23 v2 Representation Theory
Abstract
We investigate the bounded derived category of coherent sheaves on irreducible singular projective curves of arithmetic genus one. A description of the group of exact auto-equivalences and the set of all t-structures of this category is given. We describe the moduli space of stability conditions, obtain a complete classification of all spherical objects in this category and show that the group of exact auto-equivalences acts transitively on them. Harder-Narasimhan filtrations in the sense of Bridgeland are used as our main technical tool.
Keywords
Cite
@article{arxiv.math/0503496,
title = {Derived categories of irreducible projective curves of arithmetic genus one},
author = {Igor Burban and Bernd Kreussler},
journal= {arXiv preprint arXiv:math/0503496},
year = {2007}
}
Comments
44 pages; minor modifications; to appear in Compositio Math