Gauss-Manin systems of wild regular functions: Givental-Hori-Vafa models of smooth hypersurfaces in weighted projective spaces as an example

TL;DR

This paper investigates Gauss-Manin systems associated with Hori-Vafa models, which serve as mirror partners to the small quantum cohomology of smooth hypersurfaces in weighted projective spaces, focusing on non-tame Laurent polynomial functions.

Contribution

It provides a detailed analysis of Gauss-Manin systems for Hori-Vafa models, expanding understanding of mirror symmetry in the context of weighted projective hypersurfaces.

Findings

Gauss-Manin systems are characterized for non-tame Laurent polynomials.

Hori-Vafa models are confirmed as mirror partners to quantum cohomology.

Insights into the structure of Gauss-Manin systems for these models.

Abstract

We study Gauss-Manin systems of non tame Laurent polynomial functions. We focuse on Hori-Vafa models, which are the expected mirror partners of the small quantum cohomology of smooth hypersurfaces in weighted projective spaces.