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.
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Nill, B. Complete toric varieties with reductive automorphism group. Math. Z. 252, 767–786 (2006). https://doi.org/10.1007/s00209-005-0880-z
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DOI: https://doi.org/10.1007/s00209-005-0880-z