Seshadri stratifications and standard monomial theory
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arXiv
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| Format: | Preprint |
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2021
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| author | Chirivì, Rocco Fang, Xin Littelmann, Peter |
| author_facet | Chirivì, Rocco Fang, Xin Littelmann, Peter |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_03776 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Seshadri stratifications and standard monomial theory Chirivì, Rocco Fang, Xin Littelmann, Peter Algebraic Geometry Commutative Algebra Combinatorics 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. |
| title | Seshadri stratifications and standard monomial theory |
| topic | Algebraic Geometry Commutative Algebra Combinatorics |
| url | https://arxiv.org/abs/2112.03776 |