Symmetric obstruction theories and Hilbert schemes of points on threefolds

2005/12/24 by Kai Behrend, Behrend, Kai, Barbara Fantechi +1 · 5 citations
Mathematics · #14C05 #14J32 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.math/0512556

openalex publication_date 2005/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the notion of symmetric obstruction theory and study symmetric obstruction theories which are compatible with C*-actions. We prove that the contribution of an isolated fixed point under a C*-action to equivariant Donaldson-Thomas type invariants is +/- 1. As an application, we compute weighted Euler characteristics of all Hilbert schemes of points on any 3-fold. Moreover, we calculate the zero-dimensional Donaldson-Thomas invariants of any projective Calabi-Yau 3-fold. This proves a conjecture of Maulik-Nekrasov-Okounkov-Pandharipande.

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