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 achieve 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 -vectors. In this paper, as a generalization of this result, we present a characterization of all Castelnuovo polytopes. Finally, as an application of our characterization, we give a sufficient criterion for a lattice polytope to be IDP.
Citation
Akiyoshi Tsuchiya. "Castelnuovo Polytopes." Michigan Math. J. 73 (5) 899 - 908, November 2023. https://doi.org/10.1307/mmj/20216027
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