English

Deformations of Smooth Toric Surfaces

Algebraic Geometry 2011-02-23 v3

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.

Keywords

Cite

@article{arxiv.0902.0529,
  title  = {Deformations of Smooth Toric Surfaces},
  author = {Nathan Owen Ilten},
  journal= {arXiv preprint arXiv:0902.0529},
  year   = {2011}
}

Comments

15 pages, 4 figures; v3 minor changes to introduction

R2 v1 2026-06-21T12:07:32.903Z