Hall algebras and curve-counting invariants

Abstract

We use Joyce's theory of motivic Hall algebras to prove that reduced Donaldson-Thomas curve-counting invariants on Calabi-Yau threefolds coincide with stable pair invariants, and that the generating functions for these invariants are Laurent expansions of rational functions.

38 pages. Version 2 corrected an error in the published paper kindly pointed out by Yukinobu Toda. Version 3 corrects a further error pointed out by Toda and Tasuki Kinjo. The only changes are footnotes on pages 27 and 38, together with new Sections 7.3 and 7.4 which explain the mistakes and how to fix them

References in corpus (2)

• Zero dimensional Donaldson-Thomas invariants of threefolds
• Construction of Hilbert and Quot Schemes

Cited by in corpus (6)

• Motivic Donaldson-Thomas invariants of the conifold and the refined topological vertex
• Curve counting theories via stable objects I. DT/PT correspondence
• Generalized Donaldson-Thomas theory over fields K $\ne$ C
• Descendents on local curves: Stationary theory
• Multiple cover formula of generalized DT invariants I: parabolic stable pairs
• Curve counting invariants around the conifold point