Valuative invariants for linearized line bundles on a spherical variety

Abstract

We give formulas for various valuative invariants of linearized ample line bundles on a projective spherical variety. Then we show how to use these formulas to study $g$-solitons on a Fano spherical variety. As a corollary, we show that for a Fano horospherical manifold $X$, the corresponding cone $(K_X{)}^{\times }$ always admits a Calabi-Yau cone metric.

arXiv commentIn this second version, we add a section on preliminaries for spherical varieties, provide additional details throughout the article, and correct several typos