Automorphism group of a toric variety

M. T Sancho; J. P Moreno; Carlos Sancho

paper

Automorphism group of a toric variety

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 $A u t_{k}^{0} X$ 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 $A u t_{k} X / A u t_{k}^{0} X$ is a quotient of the group of automorphisms of $M$ leaving invariant the fan.