Automorphisms of products of toric varieties

TL;DR

This paper characterizes the automorphism group of a product of complete toric varieties, showing it decomposes into automorphisms of components up to permutation, and revisits Demazure's classic results using modern language.

Contribution

It provides an explicit description of automorphism groups for products of toric varieties and reestablishes Demazure's classical theorem with contemporary methods.

Findings

Automorphism group decomposes into component automorphisms and permutations.

Provides explicit formulas for automorphisms of product toric varieties.

Reproves Demazure's theorem using modern language.

Abstract

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.