Castelnuovo polytopes

Fuente: arXiv
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Auteur principal: Tsuchiya, Akiyoshi
Format: Preprint
Publié: 2020
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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