Castelnuovo spanning polytopes
2020
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 Castelnuovo polytopes under a mild assumption in terms of
their $h^*$-vectors will be presented. In particular, we characterize
Castelnuovo spanning polytopes. Finally, as an application of our
characterization, we give a necessary condition for IDP polytopes.
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