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arXiv · 2010.13617

Castelnuovo polytopes

Akiyoshi Tsuchiya
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Abstract

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.

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Akiyoshi Tsuchiya. 2020-10-26. Castelnuovo polytopes. https://doi.org/10.1307/mmj/20216027

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