Stability conditions and crepant small resolutions
Abstract
In this paper, we describe the spaces of stability conditions on the triangulated categories associated to three dimensional crepant small resolutions. The resulting spaces have chamber structures such that each chamber corresponds to a birational model together with a special Fourier-Mukai transform. We observe these spaces are covering spaces over certain open subsets of finite dimensional vector spaces, and determine their deck transformations.
Cite
@article{arxiv.math/0512648,
title = {Stability conditions and crepant small resolutions},
author = {Yukinobu Toda},
journal= {arXiv preprint arXiv:math/0512648},
year = {2007}
}
Comments
A lot of changes. Section 5 and Section 6 in the previous version are removed, and some explanations for the background are added. The statement in the original version contains a mistake, and added an assumption for a crepant small resolution. To apper in Transactions of the American Mathematical Society