Characterization of affine toric varieties by their automorphism groups

Alvaro Liendo, Andriy Regeta, Christian Urech

Published 2018-05-10Version 1

We show that complex affine toric surfaces are determined by the abstract group structure of their regular automorphism groups in the category of complex normal affine surfaces using properties of the Cremona group. As a generalization to arbitrary dimensions, we show that complex affine toric varieties, with the exception of the algebraic torus, are uniquely determined in the category of complex affine normal varieties by their automorphism groups seen as ind-groups.