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

Symmetric obstruction theories and Hilbert schemes of points on threefolds