Mirror Symmetry and smoothing Gorenstein toric affine 3-folds

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.

23 pages, 6 figures. The paper has been submitted to "Facets of Algebraic Geometry: A Volume in Honour of William Fulton's 80th Birthday"

References in corpus (2)

• Minkowski Polynomials and Mutations
• Maximally Mutable Laurent Polynomials

Cited by in corpus (3)

• On deformation spaces of toric singularities and on singularities of K-moduli of Fano varieties
• K-moduli of Fano 3-folds can have embedded points
• Symplectomorphisms of some Weinstein 4-manifolds