Complete toric varieties with reductive automorphism group |
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Authors: | Benjamin Nill |
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Institution: | 1. Mathematisches Institut, Universit?t Tübingen, Auf der Morgenstelle 10, 72076, Tübingen, Germany
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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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Keywords: | Toric varieties Algebraic groups Fano varieties Lattice polytopes |
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