Mathematical Research Letters

Volume 29 (2022)

Number 2

Automorphisms of products of toric varieties

Pages: 529 – 540



Alvaro Liendo (Instituto de Matemática y Física, Universidad de Talca, Chile)

Giancarlo Lucchini Arteche (Departamento de Matemáticas, Facultad de Ciencias. Universidad de Chile, Ñuñoa, Santiago, Chile)


We give an explicit description of the automorphism group of a product of complete toric varieties over an arbitrary field in terms of the respective automorphism groups of its components. More precisely, we prove that, up to permutation of isomorphic components, an automorphism of a product corresponds to a product of automorphisms of its components. We also reprove, in modern language, the classic result by Demazure describing the group-scheme of automorphisms of a complete toric variety over an arbitrary field.

The first author was partially supported by ANID via Fondecyt Grant 1200502. The second author was partially supported by ANID via Fondecyt Grant 1210010.

Received 22 January 2021

Accepted 23 February 2021

Published 29 September 2022