On the existence of $B$-root subgroups on affine spherical varieties

Roman Avdeev, Vladimir Zhgoon

Published 2021-12-28, updated 2022-07-10Version 2

Let $X$ be an irreducible affine algebraic variety that is spherical with respect to an action of a connected reductive group $G$. In this paper we provide sufficient conditions, formulated in terms of weight combinatorics, for the existence of one-parameter additive actions on $X$ normalized by a Borel subgroup $B \subset G$. As an application, we prove that every $G$-stable prime divisor in $X$ can be connected with the open $G$-orbit by means of a suitable $B$-normalized one-parameter additive action.