Complete toric varieties with reductive automorphism group

Details Complete toric varieties with reductive automorphism group Complete toric varieties with reductive automorphism group

2004-07-28

arxiv.org/abs/math/0407491v1

Math. Z. 252 (2006), 767-786

Mathematics

Algebraic Geometry

AMS-LaTeX, 20 pages with 1 figure

Scientific paper

10.1007/s00209-005-0880-z

We give equivalent and sufficient criteria for the automorphism group of a complete toric variety, respectively a Gorenstein toric Fano variety, to be reductive. In particular we show that the automorphism group of a Gorenstein toric Fano variety is reductive, if the barycenter of the associated reflexive polytope is zero. Furthermore a sharp bound on the dimension of the reductive automorphism group of a complete toric variety is proven by studying the set of Demazure roots.

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