Abstract:
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 an open $G$-orbit by means of a suitable $B$-normalized one-parameter additive action.
Keywords:additive group action, toric variety, spherical variety, Demazure root, locally nilpotent derivation, local structure theorem.
UDC:512.745.2
Presented:V. P. Platonov Received: 22.12.2021 Revised: 22.12.2021 Accepted: 28.12.2021