Congruences on K–theoretic Gromov–Witten invariants

Guéré, Jérémy

doi:10.2140/gt.2023.27.3585

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Congruences on K–theoretic Gromov–Witten invariants

Jérémy Guéré

Geometry & Topology 27 (2023) 3585–3618

DOI: 10.2140/gt.2023.27.3585

Abstract

We study K–theoretic Gromov–Witten invariants of projective hypersurfaces using a virtual localization formula under finite group actions. In particular, it provides all K–theoretic Gromov–Witten invariants of the quintic threefold modulo $41$ , up to genus $19$ and degree $40$ . As an illustration, we give an instance in genus one and degree one. Applying the same idea to a K–theoretic version of FJRW theory, we determine it modulo $205$ for the quintic polynomial with minimal group and narrow insertions, in every genus.

Keywords

K–theory, Gromov-Witten theory, mirror symmetry

Mathematical Subject Classification

Primary: 14N35

References

Publication

Received: 16 April 2021

Revised: 7 January 2022

Accepted: 5 February 2022

Published: 5 December 2023

Proposed: Jim Bryan

Seconded: Dan Abramovich, Richard P Thomas

Authors

Jérémy Guéré
Institut Fourier CNRS Université de Grenoble Alpes Grenoble France

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Volume 27, issue 9 (2023)