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Genus zero Gopakumar-Vafa invariants of contractible curves

Sheldon Katz
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Abstract

A version of the Donaldson-Thomas invariants of a Calabi-Yau threefold is proposed as a conjectural mathematical definition of the Gopakumar-Vafa invariants. These invariants have a local version, which is verified to satisfy the required properties for contractible curves. This provides a new viewpoint on the computation of the local Gromov-Witten invariants of contractible curves by Bryan, Leung, and the author.

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Sheldon Katz. 2006-01-09. Genus zero Gopakumar-Vafa invariants of contractible curves. https://arxiv.org/abs/math/0601193

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