Complete toric varieties with reductive automorphism group
arXiv:math/0407491 · doi:10.1007/s00209-005-0880-z
Abstract
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.
AMS-LaTeX, 20 pages with 1 figure