A proof of the Donaldson-Thomas crepant resolution conjecture

• 成果类型: Article
• 署名作者: Beentjes, Sjoerd Viktor; Calabrese, John; Rennemo, Jorgen Vold
• 署名单位: University of Edinburgh; Heriot Watt University; University of Edinburgh; University of Oslo
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01109-w
• 发表日期: 2022
• 页码: 451-562
• 关键词: abelian categories; hilbert schemes; wall-crossings; stable objects; hall algebras; configurations; INVARIANTS; STABILITY; bundles; MODULI

摘要

We prove the crepant resolution conjecture for Donaldson-Thomas invariants of hard Lefschetz 3-Calabi-Yau (CY3) orbifolds, formulated by Bryan-Cadman-Young, interpreting the statement as an equality of rational functions. In order to do so, we show that the generating series of stable pair invariants on any CY3 orbifold is the expansion of a rational function. As a corollary, we deduce a symmetry of this function induced by the derived dualising functor. Our methods also yield a proof of the orbifold DT/PT correspondence for multi-regular curve classes on hard Lefschetz CY3 orbifolds.