Some examples of non-smoothable Gorenstein Fano toric threefolds

Abstract

We present a combinatorial criterion on reflexive polytopes of dimension 3 which gives a local-to-global obstruction for the smoothability of the corresponding Fano toric threefolds. As a result, we show examples of singular Gorenstein Fano toric threefolds which have compound Du Val, hence smoothable, singularities but are not smoothable.

11 pages, 2 figures

References in corpus (3)

• Minkowski Polynomials and Mutations
• Mirror Symmetry and the Classification of Orbifold del Pezzo Surfaces
• Mutations of Laurent Polynomials and Flat Families with Toric Fibers

Cited by in corpus (1)

• On toric geometry and K-stability of Fano varieties