Seshadri stratifications and standard monomial theory

• 成果类型: Article
• 署名作者: Chirivi, Rocco; Fang, Xin; Littelmann, Peter
• 署名单位: University of Salento; RWTH Aachen University; University of Cologne
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-023-01206-4
• 发表日期: 2023
• 页码: 489-572
• 关键词: g-p; geometry; bases; normality; ALGEBRAS; bodies

摘要

We introduce the notion of a Seshadri stratification on an embedded projective variety. Such a structure enables us to construct a Newton-Okounkov simplicial complex and a flat degeneration of the projective variety into a union of toric varieties. We show that the Seshadri stratification provides a geometric setup for a standard monomial theory. In this framework, Lakshmibai-Seshadri paths for Schubert varieties get a geometric interpretation as successive vanishing orders of regular functions.