Deformations of smooth toric surfaces
Tóm tắt
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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