Homogeneous spherical data of orbits in spherical embeddings

Abstract

Let $G$ be a connected reductive complex algebraic group. Luna assigned to any spherical homogeneous space $G/H$ a combinatorial object called a homogeneous spherical datum. By a theorem of Losev, this object uniquely determines $G/H$ up to $G$-equivariant isomorphism. In this paper, we determine the homogeneous spherical datum of a $G$-orbit $X_0$ in a spherical embedding $G/H\hookrightarrow X$. As an application, we obtain a description of the colored fan associated to the spherical embedding $X_0\hookrightarrow \overline{X_0}$.

14 pages, 1 table

Cited by in corpus (3)

• K{ä}hler geometry of horosymmetric varieties, and application to Mabuchi's K-energy functional
• Gorenstein spherical Fano varieties
• K-stable valuations and Calabi-Yau metrics on affine spherical varieties