Deformations of Rational T-Varieties

Details Deformations of Rational T-Varieties Deformations of Rational T-Varieties

2009-03-08

arxiv.org/abs/0903.1393v3

Mathematics

Algebraic Geometry

22 pages, 9 figures; v2 minor changes to introduction; v3 some corrections, to appear in Journal of Algebraic Geometry

Scientific paper

We show how to construct certain homogeneous deformations for rational normal varieties with codimension one torus action. This can then be used to construct homogeneous deformations of any toric variety in arbitrary degree. For locally trivial deformations coming from this construction, we calculate the image of the Kodaira-Spencer map. We then show that for a smooth complete toric variety, our homogeneous deformations span the space of first-order deformations.

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