New kinds of block diagonal matching fields and toric degenerations of Grassmannians
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916715853512704 |
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| author | Higashitani, Akihiro Kowaki, Nobukazu |
| author_facet | Higashitani, Akihiro Kowaki, Nobukazu |
| contents | Block diagonal matching field has many previous works. In general, a coherent matching field induces a monomial order to Plücker algebra, and block diagonal matching fields are a kind of coherent matching fields. In the present paper, we introduce a new kind of block diagonal matching fields and study the problem when they give a SAGBI basis. As a corollary, we provide a new family of toric degenerations of Grassmannians by using SAGBI bases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00388 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New kinds of block diagonal matching fields and toric degenerations of Grassmannians Higashitani, Akihiro Kowaki, Nobukazu Combinatorics Commutative Algebra Block diagonal matching field has many previous works. In general, a coherent matching field induces a monomial order to Plücker algebra, and block diagonal matching fields are a kind of coherent matching fields. In the present paper, we introduce a new kind of block diagonal matching fields and study the problem when they give a SAGBI basis. As a corollary, we provide a new family of toric degenerations of Grassmannians by using SAGBI bases. |
| title | New kinds of block diagonal matching fields and toric degenerations of Grassmannians |
| topic | Combinatorics Commutative Algebra |
| url | https://arxiv.org/abs/2505.00388 |