Negative deformations of toric singularities that are smooth in codimension two

2011/09/15 by Altmann, Klaus, Kastner, Lars
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1109.3344

Abstract

Given a polyhedral cone sigma with smooth two-dimensional faces and, moreover, a lattice point R in the dual cone of sigma, we describe the part of the versal deformation of the associated toric variety TV(sigma) that is built from the deformation parameters of multidegree R. Let Q the polyhedron obtained by intersecting sigma with the hyperplane R=1. Then the base space is (the germ of) an affine scheme that reflects certain possibilities of splitting Q into Minkowski summands.

Related

• Versality in toric geometry
• One-parameter families containing three-dimensional toric Gorenstein singularities
• Toric Q-Gorenstein Singularities
• Deformations of Toric Varieties via Minkowski Sum Decompositions of Polyhedral Complexes
• The versal Deformation of an isolated toric Gorenstein Singularity