Semi-Perfect Obstruction theory and DT Invariants of Derived Objects

2011/05/17 by Huai-Liang Chang, Jun Li, Chang, Huai-liang +1 · 2 citations
Mathematics · #14N35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1105.3261

openalex publication_date 2011/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce semi-perfect obstruction theory of a Deligne-Mumford stack X consisting of local perfect obstruction theories with weak comparisons on overlaps. We show that semi-perfect obstruction theory shares similar properties with perfect obstruction theory. We use semi-perfect obstruction theory to construct virtual cycles of moduli of derived objects on Calabi-Yau threefolds. In the revision, we assume the existence of obstruction sheaf and put the (coarse moduli of the) intrinsic normal cone inside the obstruction sheaf. This avoids the issue of descent of bundle stacks of the local obstruction complexes.

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