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arXiv · 2112.03776

Seshadri stratifications and standard monomial theory

Rocco Chirivì·Xin Fang·Peter Littelmann
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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.

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Rocco Chirivì, Xin Fang, Peter Littelmann. 2023-06-22. Seshadri stratifications and standard monomial theory. https://doi.org/10.1007/s00222-023-01206-4

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