Congruences on K–theoretic Gromov–Witten invariants

Guéré, Jérémy¹

¹ Institut Fourier, CNRS, Université de Grenoble Alpes, Grenoble, France

Geometry & topology, Tome 27 (2023) no. 9, pp. 3585-3618.

Résumé

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.

Détail

DOI : 10.2140/gt.2023.27.3585

Keywords: K–theory, Gromov-Witten theory, mirror symmetry

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