Jason Lo and Zhenbo Qin, Mini-walls for Bridgeland stability conditions on the derived category of sheaves over surfaces, Asian J.Dominic Joyce and Yinan Song, A theory of generalized Donaldson-Thomas invariants, Mem.Dominic Joyce, Motivic invariants of Artin stacks and ‘stack functions’, Q.Stability conditions and identities, Adv. Dominic Joyce, Configurations in abelian categories.Jun-ichi Igusa, A classification of spinors up to dimension twelve, Amer.Huybrechts, Fourier-Mukai transforms in algebraic geometry, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, Oxford, 2006. Gulbrandsen, Donaldson-Thomas invariants for complexes on abelian threefolds, Math. Jim Bryan, Georg Oberdieck, Rahul Pandharipande, and Qizheng Yin, Curve counting on abelian surfaces and threefolds, Algebr. Tom Bridgeland, Hall algebras and curve-counting invariants, J.Tom Bridgeland, Stability conditions on triangulated categories, Ann.Lange, The dual polarization of an abelian variety, Arch. Kai Behrend, Donaldson-Thomas type invariants via microlocal geometry, Ann.Oberdieck, On equivariant derived categories, arXiv: 2006.13626 (2020). Arend Bayer, Emanuele Macrì, and Yukinobu Toda, Bridgeland stability conditions on threefolds I: Bogomolov-Gieseker type inequalities, J.Arend Bayer, Emanuele Macrì, and Paolo Stellari, The space of stability conditions on abelian threefolds, and on some Calabi-Yau threefolds, Invent.Fourier (Grenoble) 63 (2013), no. 6, 2349–2402 (English, with English and French summaries). Jarod Alper, Good moduli spaces for Artin stacks, Ann.Heinloth, Existence of moduli space for algebraic stacks, arXiv: 1812.01128 (2018). A definition of reduced generalized Donaldson–Thomas invariants for arbitrary Calabi–Yau threefolds with abelian actions is given. We also prove the existence of a Gieseker chamber and determine all wall-crossing contributions. In particular, the stability manifold is non-empty. We show that certain previously constructed stability conditions satisfy the full support property. The discussion yields evidence for a conjectural formula for curve counting invariants by Bryan, Pandharipande, Yin, and the first author.įor the proof we strengthen several known results on Bridgeland stability conditions of abelian threefolds. For principally polarized abelian threefolds of Picard rank one, the wall-crossing contributions are discussed in detail. We also present a numerical criterion for the absence of walls in terms of a discriminant function. The main result is the invariance of the reduced Donaldson–Thomas invariants under all derived autoequivalences, up to explicitly given wall-crossing terms. We study the reduced Donaldson–Thomas theory of abelian threefolds using Bridgeland stability conditions. Donaldson–Thomas invariants of abelian threefolds and Bridgeland stability conditionsĪuthors: Georg Oberdieck, Dulip Piyaratne and Yukinobu Toda
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