Automorphism group of a toric variety

2018/09/24 by Sancho, M. T, Moreno, J. P, Sancho, Carlos
#14L15 #14L17 #14L30 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.09070

Abstract

We calculate the automorphism group of a complete toric variety X with torus T_M. We prove that the radical unipotent of Aut_k⁰X is a semidirect product of additive groups, the reductive part is a quotient of a product of lineal groups and we give the action of linear groups on the additive groups. We also prove that Aut_kX/Aut_k⁰X is a quotient of the group of automorphisms of M leaving invariant the fan.

Related

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• Characterization of affine surfaces with a torus action by their automorphism groups