Multiple cover formula of generalized DT invariants II: Jacobian localizations

2011/08/25 by Yukinobu Toda, Toda, Yukinobu · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Advanced Differential Equations and Dynamical Systems #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1108.4993

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.

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