arXiv:1310.0299 Abstract | arXiv Analytics

arXiv:1310.0299 [math.AG]Abstract References Reviews Resources

Fourier-Mukai Transforms and Bridgeland Stability Conditions on Abelian Threefolds II

Published 2013-10-01, updated 2015-11-22Version 2

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.

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

Categories: math.AG

Subjects: 14F05, 14J30, 14J32, 14J60, 14K99, 18E30, 18E35, 18E40

Keywords: bridgeland stability conditions, fourier-mukai transform, abelian threefolds, strong bogomolov-gieseker type inequality, tilt stable objects satisfy

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