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