Symmetric obstruction theories and Hilbert schemes of points on threefolds

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.

Cited by in corpus (10)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Calabi-Yau algebras
• Zero dimensional Donaldson-Thomas invariants of threefolds
• Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants
• Motivic Donaldson-Thomas invariants of the conifold and the refined topological vertex
• Wall Crossing Phenomenology of Orientifolds
• Algebraic cobordism revisited
• Super-rigid Donaldson-Thomas invariants
• The Gromov-Witten and Donaldson-Thomas correspondence for trivial elliptic fibrations
• Genus zero Gopakumar-Vafa invariants of contractible curves