Symplectomorphism group relations and degenerations of Landau-Ginzburg models

TL;DR

This paper explores the relations in symplectomorphism groups of toric hypersurfaces and connects these to degenerations of Landau-Ginzburg models, offering new insights into mirror symmetry and the minimal model program.

Contribution

It constructs a stack of toric hypersurfaces with boundary to explicitly describe symplectomorphism relations and links these to Landau-Ginzburg degenerations in mirror symmetry.

Findings

Explicit relations in symplectomorphism groups derived from degenerations.

New perspective on mirror symmetry via Landau-Ginzburg model degenerations.

Connections to the minimal model program through mirror symmetry.

Abstract

In this paper, we describe explicit relations in the symplectomorphism groups of toric hypersurfaces. To define the elements involved, we construct a proper stack of toric hypersurfaces with compactifying boundary representing toric hypersurface degenerations. Our relations arise through the study of the one dimensional strata of this stack. The results are then examined from the perspective of homological mirror symmetry where we view sequences of relations as maximal degenerations of Landau-Ginzburg models. We then study the B-model mirror to these degenerations, which gives a new mirror symmetry approach to the minimal model program.