Permutation-equivariant quantum K-theory of Fermat singularities
Abstract
We compute the genus-0 permutation-equivariant quantum K-theory of Fermat singularities, in parallel with the Givental-Lee theory for projective varieties. We extend Givental-Tonita's formalism of adelic Lagrangian cones to the singularity theory, and we obtain explicit -functions for the invariants, which satisfy the same -difference equation as Givental's -function of the associated hypersurface. This can be regarded as an extension of the Landau-Ginzburg/Calabi-Yau correspondence, although a discrepancy between the two sides sides emerges in K-theory. In the case of the quintic threefold, both generating functions satisfy a -difference equation of degree ; the hypersurface -function only spans a -dimensional subspace of solutions, while the singularity -function spans the full space of solutions.
Keywords
Cite
@article{arxiv.2410.17730,
title = {Permutation-equivariant quantum K-theory of Fermat singularities},
author = {Maxime Cazaux},
journal= {arXiv preprint arXiv:2410.17730},
year = {2026}
}