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arXiv · 0902.0529

Deformations of Smooth Toric Surfaces

Nathan Owen Ilten
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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.

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Nathan Owen Ilten. 2009-04-08. Deformations of Smooth Toric Surfaces. https://doi.org/10.1007/s00229-010-0386-9

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