Combinatorial Seshadri stratifications on normal toric varieties
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918007990648832 |
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| author | Chirivì, Rocco Cesari, Martina Costa Fang, Xin Littelmann, Peter |
| author_facet | Chirivì, Rocco Cesari, Martina Costa Fang, Xin Littelmann, Peter |
| contents | We apply the theory of Seshadri stratifications to embedded toric varieties $X_P\subseteq \mathbb P(V)$ associated with a normal lattice polytope $P$. The approach presented here is purely combinatorial and completely independent of \cite{CFL}. In particular, we get a close connection between a certain class of triangulations of the polytope $P$, Seshadri stratifications of $X_P$ arising from torus orbit closures, and the associated degenerate semi-toric varieties. In the last section we show that the approach here and the one in \cite{CFL} produce the same quasi-valuations and hence the same degenerations of $X_P$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_16161 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Combinatorial Seshadri stratifications on normal toric varieties Chirivì, Rocco Cesari, Martina Costa Fang, Xin Littelmann, Peter Algebraic Geometry Combinatorics We apply the theory of Seshadri stratifications to embedded toric varieties $X_P\subseteq \mathbb P(V)$ associated with a normal lattice polytope $P$. The approach presented here is purely combinatorial and completely independent of \cite{CFL}. In particular, we get a close connection between a certain class of triangulations of the polytope $P$, Seshadri stratifications of $X_P$ arising from torus orbit closures, and the associated degenerate semi-toric varieties. In the last section we show that the approach here and the one in \cite{CFL} produce the same quasi-valuations and hence the same degenerations of $X_P$. |
| title | Combinatorial Seshadri stratifications on normal toric varieties |
| topic | Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2501.16161 |