Symmetric obstruction theories and Hilbert schemes of points on threefolds

Details Symmetric obstruction theories and Hilbert schemes of points on threefolds Symmetric obstruction theories and Hilbert schemes of points on threefolds

2005-12-24

arxiv.org/abs/math/0512556v1

Mathematics

Algebraic Geometry

Scientific paper

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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