Donaldson-Thomas invariants of abelian threefolds and Bridgeland stability conditions

• Verfasst von: Oberdieck, Georg [VerfasserIn]
• Verfasst von: Piyaratne, Dulip [VerfasserIn]
• Verfasst von: Toda, Yukinobu [VerfasserIn]
• Titel: Donaldson-Thomas invariants of abelian threefolds and Bridgeland stability conditions
• Verf.angabe: Georg Oberdieck, Dulip Piyaratne, and Yukinobu Toda
• Jahr: 2022
• Umfang: 61 S.
• Fussnoten: Online veröffentlicht: 14. September 2021 ; Gesehen am 12.12.2024
• Titel Quelle: Enthalten in: Journal of algebraic geometry
• Ort Quelle: Providence, RI : Univ. Press, 2002
• Jahr Quelle: 2022
• Band/Heft Quelle: 31(2022), 1, Seite 13-73
• ISSN Quelle: 1534-7486
• DOI: doi:10.1090/jag/788
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1912178311

Abstract

Abstract: We study the reduced Donaldson–Thomas theory of abelian threefolds using Bridgeland stability conditions. The main result is the invariance of the reduced Donaldson–Thomas invariants under all derived autoequivalences, up to explicitly given wall-crossing terms. We also present a numerical criterion for the absence of walls in terms of a discriminant function. For principally polarized abelian threefolds of Picard rank one, the wall-crossing contributions are discussed in detail. The discussion yields evidence for a conjectural formula for curve counting invariants by Bryan, Pandharipande, Yin, and the first author. For the proof we strengthen several known results on Bridgeland stability conditions of abelian threefolds. We show that certain previously constructed stability conditions satisfy the full support property. In particular, the stability manifold is non-empty. We also prove the existence of a Gieseker chamber and determine all wall-crossing contributions. A definition of reduced generalized Donaldson–Thomas invariants for arbitrary Calabi–Yau threefolds with abelian actions is given.