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.
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