Birational maps to Grassmannians, representations and poset polytopes
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911798611935232 |
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| author | Feigin, Evgeny Samotij, with an appendix in collaboration with Wojciech |
| author_facet | Feigin, Evgeny Samotij, with an appendix in collaboration with Wojciech |
| contents | We study the closure of the graph of the birational map from a projective space to a Grassmannian. We provide explicit description of the graph closure and compute the fibers of the natural projection to the Grassmannian. We construct embeddings of the graph closure to the projectivizations of certain cyclic representations of a degenerate special linear Lie algebra and study algebraic and combinatorial properties of these representations. In particular, we describe monomial bases, generalizing the FFLV bases. The proof relies on combinatorial properties of a new family of poset polytopes, which are of independent interest. As a consequence we obtain flat toric degenerations of the graph closure studied by Borovik, Sturmfels and Sverrisdóttir. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10074 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Birational maps to Grassmannians, representations and poset polytopes Feigin, Evgeny Samotij, with an appendix in collaboration with Wojciech Algebraic Geometry Combinatorics Representation Theory We study the closure of the graph of the birational map from a projective space to a Grassmannian. We provide explicit description of the graph closure and compute the fibers of the natural projection to the Grassmannian. We construct embeddings of the graph closure to the projectivizations of certain cyclic representations of a degenerate special linear Lie algebra and study algebraic and combinatorial properties of these representations. In particular, we describe monomial bases, generalizing the FFLV bases. The proof relies on combinatorial properties of a new family of poset polytopes, which are of independent interest. As a consequence we obtain flat toric degenerations of the graph closure studied by Borovik, Sturmfels and Sverrisdóttir. |
| title | Birational maps to Grassmannians, representations and poset polytopes |
| topic | Algebraic Geometry Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2403.10074 |