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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Ilten, N.O. Deformations of smooth toric surfaces. manuscripta math. 134, 123–137 (2011). https://doi.org/10.1007/s00229-010-0386-9
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DOI: https://doi.org/10.1007/s00229-010-0386-9