Fourier-Mukai Transforms and Bridgeland Stability Conditions on Abelian Threefolds

Antony Maciocia, Dulip Piyaratne

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Pages (from-to)270-297
Number of pages28
JournalAlgebraic Geometry
Volume2
Issue number3
DOIs
Publication statusPublished - 3 Dec 2015

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