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Published July 9, 2019 | Accepted Version
Journal Article Open

Local Gromov-Witten invariants are log invariants

Abstract

We prove a simple equivalence between the virtual count of rational curves in the total space of an anti-nef line bundle and the virtual count of rational curves maximally tangent to a smooth section of the dual line bundle. We conjecture a generalization to direct sums of line bundles.

Additional Information

© 2019 Elsevier. Received 8 March 2018, Revised 4 February 2019, Accepted 22 April 2019, Available online 9 May 2019. Communicated by Tony Pantev. This work was supported by HR's Deutsche Forschungsgemeinschaft Emmy-Noether grant RU1629/4-1. We are grateful to Dan Abramovich, Mark Gross, Davesh Maulik, Rahul Pandharipande and James Pascaleff for helpful and inspiring discussions, and to the anonymous referee for valuable suggestions.

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August 22, 2023
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October 20, 2023