Newton-Okounkov polytopes of Schubert varieties arising from cluster structures
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866911073237467136 |
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| author | Fujita, Naoki Oya, Hironori |
| author_facet | Fujita, Naoki Oya, Hironori |
| contents | The theory of Newton-Okounkov bodies is a generalization of that of Newton polytopes for toric varieties, and it gives a systematic method of constructing toric degenerations of projective varieties. In this paper, we study Newton-Okounkov bodies of Schubert varieties from the theory of cluster algebras. We construct Newton-Okounkov bodies using specific valuations which generalize extended g-vectors in cluster theory, and discuss how these bodies are related to string polytopes and Nakashima-Zelevinsky polytopes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2002_09912 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Newton-Okounkov polytopes of Schubert varieties arising from cluster structures Fujita, Naoki Oya, Hironori Representation Theory Algebraic Geometry Combinatorics 05E10 (Primary) 13F60, 14M15, 14M25, 52B20 (Secondary) The theory of Newton-Okounkov bodies is a generalization of that of Newton polytopes for toric varieties, and it gives a systematic method of constructing toric degenerations of projective varieties. In this paper, we study Newton-Okounkov bodies of Schubert varieties from the theory of cluster algebras. We construct Newton-Okounkov bodies using specific valuations which generalize extended g-vectors in cluster theory, and discuss how these bodies are related to string polytopes and Nakashima-Zelevinsky polytopes. |
| title | Newton-Okounkov polytopes of Schubert varieties arising from cluster structures |
| topic | Representation Theory Algebraic Geometry Combinatorics 05E10 (Primary) 13F60, 14M15, 14M25, 52B20 (Secondary) |
| url | https://arxiv.org/abs/2002.09912 |