Generalized Donaldson-Thomas Invariants via Kirwan Blowups

2017/12/07 by Young‐Hoon Kiem, Jun Li, Kiem, Young-Hoon +3 · 1 citation
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1712.02544

Abstract

We develop a virtual cycle approach towards generalized Donaldson-Thomas theory of Calabi-Yau threefolds. Let M be the moduli stack of Gieseker semistable sheaves of fixed topological type on a Calabi-Yau threefold W. We construct an associated Deligne-Mumford stack \widetildeM with an induced semi-perfect obstruction theory of virtual dimension zero and define the generalized Donaldson-Thomas invariant of W via Kirwan blowups to be the degree of the virtual cycle [\widetildeM]^vir. We show that it is invariant under deformations of the complex structure of W.

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