Mirror Symmetry and smoothing Gorenstein toric affine 3-folds

TL;DR

This paper proposes conjectures linking mirror symmetry to the smoothing components of Gorenstein toric affine 3-folds, using combinatorial Laurent polynomials called 0-mutable polynomials, supported by initial evidence.

Contribution

It introduces two conjectures that connect mirror symmetry with the combinatorial classification of smoothing components in Gorenstein toric affine 3-folds.

Findings

Conjectures relate smoothing components to 0-mutable polynomials.

Evidence supports the proposed conjectures.

Framework bridges mirror symmetry and toric geometry.

Abstract

We state two conjectures that together allow one to describe the set of smoothing components of a Gorenstein toric affine 3-fold in terms of a combinatorially defined and easily studied set of Laurent polynomials called 0-mutable polynomials. We explain the origin of the conjectures in mirror symmetry and present some of the evidence.