Symmetric obstruction theories and Hilbert schemes of points on threefolds
Algebraic Geometry
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0512556,
title = {Symmetric obstruction theories and Hilbert schemes of points on threefolds},
author = {Kai Behrend and Barbara Fantechi},
journal= {arXiv preprint arXiv:math/0512556},
year = {2007}
}