On orbits of automorphism groups on horospherical varieties

Abstract

In this paper we describe orbits of automorphism group on a horospherical variety in terms of degrees of homogeneous with respect to natural grading locally nilpotent derivations. In case of (may be nonnormal) toric varieties a description of orbits of automorphism group in terms of corresponding weight monoid is obtained.

Automorphism group orbits on horospherical varieties and divisor class group

“…The main result of this paper is the following theorem. In [3] the Aut(X) 0 -orbits for an affine horospherical variety of complexity zero were investigated. Proposition 2.…”