Deformations of Smooth Toric Surfaces

Abstract

For a complete, smooth toric variety Y, we describe the graded vector space T_Y^1. Furthermore, we show that smooth toric surfaces are unobstructed and that a smooth toric surface is rigid if and only if it is Fano. For a given toric surface we then construct homogeneous deformations by means of Minkowski decompositions of polyhedral subdivisions, compute their images under the Kodaira-Spencer map, and show that they span T_Y^1.

15 pages, 4 figures; v3 minor changes to introduction

References in corpus (1)

• One-Parameter Toric Deformations of Cyclic Quotient Singularities

Cited by in corpus (8)

• Deformations of Rational T-Varieties
• Families of Invariant Divisors on Rational Complexity-One T-Varieties
• On deformation spaces of toric singularities and on singularities of K-moduli of Fano varieties
• Deformations of Smooth Complete Toric Varieties: Obstructions and the Cup Product
• Homogeneous deformations of toric pairs
• Deformations of extremal toric manifolds
• Comparison theorems for deformation functors via invariant theory
• Foldable fans, cscK surfaces and local K-moduli