Automorphism group of a toric variety

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

Automorphism group of a toric variety

Algebraic Geometry 2018-09-25 v1

Authors: M. T Sancho , J. P Moreno , Carlos Sancho

Abstract

We calculate the automorphism group of a complete toric variety $X$ with torus $T_M$ . We prove that the radical unipotent of $Aut_k^0X$ 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 $Aut_kX/Aut_k^0X$ is a quotient of the group of automorphisms of $M$ leaving invariant the fan.

Keywords

toric variety automorphism group fan semidirect product reductive group unipotent radical

Cite

@article{arxiv.1809.09070,
  title  = {Automorphism group of a toric variety},
  author = {M. T Sancho and J. P Moreno and Carlos Sancho},
  journal= {arXiv preprint arXiv:1809.09070},
  year   = {2018}
}

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