Fourier-Mukai Transforms and Bridgeland Stability Conditions on Abelian Threefolds II
Algebraic Geometry
2015-11-24 v2
Abstract
We show that the conjectural construction proposed by Bayer, Bertram, Macr\'i and Toda gives rise to Bridgeland stability conditions for a principally polarized abelian three-fold with Picard rank one by proving that tilt stable objects satisfy the strong Bogomolov-Gieseker type inequality. This is done by showing any Fourier-Mukai transform gives an equivalence of abelian categories which are double tilts of coherent sheaves.
Keywords
Cite
@article{arxiv.1310.0299,
title = {Fourier-Mukai Transforms and Bridgeland Stability Conditions on Abelian Threefolds II},
author = {Antony Maciocia and Dulip Piyaratne},
journal= {arXiv preprint arXiv:1310.0299},
year = {2015}
}
Comments
24 pages, Spurious part of Props 5.5. and 5.6 removed and text adjusted. Contact details and references updated. Additional explanations added to note 3.2 and several minor corrections made following the referee's suggestions. To appear in Inter. J. Math