The space of stability conditions on abelian threefolds, and on some Calabi-Yau threefolds

• 成果类型: Article
• 署名作者: Bayer, Arend; Macri, Emanuele; Stellari, Paolo
• 署名单位: University of Edinburgh; University of Edinburgh; Heriot Watt University; University System of Ohio; Ohio State University; Northeastern University; University of Milan
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0665-5
• 发表日期: 2016
• 页码: 869-933
• 关键词: gieseker-type inequality; REGULARITY; objects

摘要

We describe a connected component of the space of stability conditions on abelian threefolds, and on Calabi-Yau threefolds obtained as (the crepant resolution of) a finite quotient of an abelian threefold. Our proof includes the following essential steps:We simultaneously strengthen a conjecture by the first two authors and Toda, and prove that it follows from a more natural and seemingly weaker statement. This conjecture is a Bogomolov-Gieseker type inequality involving the third Chern character of tilt-stable two-term complexes on smooth projective threefolds; we extend it from complexes of tilt-slope zero to arbitrary tilt-slope. We show that this stronger conjecture implies the so-called support property of Bridgeland stability conditions, and the existence of an explicit open subset of the space of stability conditions. We prove our conjecture for abelian threefolds, thereby reproving and generalizing a result by Maciocia and Piyaratne.