Multiple cover formula of generalized DT invariants II: Jacobian localizations

Abstract

The generalized Donaldson-Thomas invariants counting one dimensional semistable sheaves on Calabi-Yau 3-folds are conjectured to satisfy a certain multiple cover formula. This conjecture is equivalent to Pandharipande-Thomas's strong rationality conjecture on the generating series of stable pair invariants, and its local version is enough to prove. In this paper, using Jacobian localizations and parabolic stable pair invariants introduced in the previous paper, we reduce the conjectural multiple cover formula for local curves with at worst nodal singularities to the case of local trees of smooth rational curves.

54pages, 3figures

References in corpus (5)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Donaldson-Thomas invariants via microlocal geometry
• Counting invariants for the ADE McKay quivers
• Multiple cover formula of generalized DT invariants I: parabolic stable pairs
• Stable pairs on local K3 surfaces

Cited by in corpus (5)

• Genus zero Gopakumar-Vafa type invariants for Calabi-Yau 4-folds
• Curve counting on elliptic Calabi-Yau threefolds via derived categories
• Tautological stable pair invariants of Calabi-Yau 4-folds
• Gopakumar-Vafa invariants via vanishing cycles
• Multiple cover formula of generalized DT invariants I: parabolic stable pairs