English

Seshadri stratifications and standard monomial theory

Algebraic Geometry 2024-04-10 v2 Commutative Algebra Combinatorics

Abstract

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.

Keywords

Cite

@article{arxiv.2112.03776,
  title  = {Seshadri stratifications and standard monomial theory},
  author = {Rocco Chirivì and Xin Fang and Peter Littelmann},
  journal= {arXiv preprint arXiv:2112.03776},
  year   = {2024}
}

Comments

76 pages

R2 v1 2026-06-24T08:07:44.811Z