Fourier-Mukai Transforms and Bridgeland Stability Conditions on Abelian Threefolds
Abstract
We show that the construction of Bayer, Bertram, Macri and Toda gives rise to a Bridgeland stability condition on a principally polarized abelian threefold with Picard rank one by establishing their conjectural generalized Bogomolov-Gieseker inequality for certain tilt stable objects. We do this by proving that a suitable Fourier-Mukai transform preserves the heart of a particular conjectural stability condition. We also show that the only reflexive sheaves with zero first and second Chern classes are the flat line bundles.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2013
- DOI:
- 10.48550/arXiv.1304.3887
- arXiv:
- arXiv:1304.3887
- Bibcode:
- 2013arXiv1304.3887M
- Keywords:
-
- Mathematics - Algebraic Geometry;
- 14F05;
- 14J30;
- 14J32;
- 14J60;
- 14K99;
- 18E30;
- 18E35;
- 18E40
- E-Print:
- Minor improvements. Paper to appear in Alg. Geom