Castelnuovo polytopes
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arXiv
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866918510463025152 |
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| author | Tsuchiya, Akiyoshi |
| author_facet | Tsuchiya, Akiyoshi |
| contents | It is known that the sectional genus of a polarized variety has an upper bound, which is an extension of the Castelnuovo bound on the genus of a projective curve. Polarized varieties whose sectional genus achieves this bound are called Castelnuovo. On the other hand, a lattice polytope is called Castelnuovo if the associated polarized toric variety is Castelnuovo. Kawaguchi characterized Castelnuovo polytopes having interior lattice points in terms of their $h^*$-vectors. In this paper, as a generalization of this result, a characterization of all Castelnuovo polytopes will be presented. Finally, as an application of our characterization, we give a sufficient criterion for a lattice polytope to be IDP. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_13617 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Castelnuovo polytopes Tsuchiya, Akiyoshi Combinatorics Algebraic Geometry 14M25, 52B20 It is known that the sectional genus of a polarized variety has an upper bound, which is an extension of the Castelnuovo bound on the genus of a projective curve. Polarized varieties whose sectional genus achieves this bound are called Castelnuovo. On the other hand, a lattice polytope is called Castelnuovo if the associated polarized toric variety is Castelnuovo. Kawaguchi characterized Castelnuovo polytopes having interior lattice points in terms of their $h^*$-vectors. In this paper, as a generalization of this result, a characterization of all Castelnuovo polytopes will be presented. Finally, as an application of our characterization, we give a sufficient criterion for a lattice polytope to be IDP. |
| title | Castelnuovo polytopes |
| topic | Combinatorics Algebraic Geometry 14M25, 52B20 |
| url | https://arxiv.org/abs/2010.13617 |