Deformations of Smooth Toric Surfaces

Details Deformations of Smooth Toric Surfaces Deformations of Smooth Toric Surfaces

2009-02-03

arxiv.org/abs/0902.0529v3

Manuscripta Mathematica 134 (2011) pp. 123-137

Mathematics

Algebraic Geometry

15 pages, 4 figures; v3 minor changes to introduction

Scientific paper

10.1007/s00229-010-0386-9

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.

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