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Symmetric obstruction theories and Hilbert schemes of points on threefolds

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arxiv math/0512556 v1 pith:DGWSCGAC submitted 2005-12-24 math.AG

Kai Behrend , Barbara Fantechi This is my paper · ORCID
classification math.AG
keywords obstructionsymmetricdonaldson-thomasfoldhilbertinvariantspointsschemes
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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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    Gopakumar–Vafa invariants are transported across Hanany–Witten transitions after removing a universal parallel-brane sector, giving first-time high-degree invariants for local dP4.

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