Standard monomial theory for wonderful varieties

TL;DR

This paper develops a standard monomial theory framework for wonderful varieties, demonstrating how the Cox ring degenerates to a multicone over a partial flag variety and establishing its rational singularities.

Contribution

It introduces a general standard monomial theory for wonderful varieties and applies it to analyze the Cox ring's structure and singularities.

Findings

Cox ring degenerates to a multicone over a partial flag variety

Cox ring has rational singularities

Provides a new degeneration technique for wonderful varieties

Abstract

A general setting for a standard monomial theory on a multiset is introduced and applied to the Cox ring of a wonderful variety. This gives a degeneration result of the Cox ring to a multicone over a partial flag variety. Further, we deduce that the Cox ring has rational singularities.