Characterizing quasiaffine spherical varieties via the automorphism group
Abstract
Let $G$ be a connected reductive algebraic group. In this note we prove that for a quasiaffine $G$spherical variety the weight monoid is determined by the weights of its nontrivial $\mathbb{G}_a$actions that are homogeneous with respect to a Borel subgroup of $G$. As an application we get that a smooth affine $G$spherical variety that is nonisomorphic to a torus is determined by its automorphism group inside the category of smooth affine irreducible varieties.
 Publication:

arXiv eprints
 Pub Date:
 November 2019
 arXiv:
 arXiv:1911.10896
 Bibcode:
 2019arXiv191110896R
 Keywords:

 Mathematics  Algebraic Geometry;
 14R20;
 14M27;
 14J50;
 22F50
 EPrint:
 Comments are welcome!