标题： 卡斯特尔诺沃多面体 显示英文标题

标题： Castelnuovo polytopes

摘要： 已知极化流形的截面亏格有一个上界，这是对射影曲线的Castelnuovo亏界的一个扩展。 截面亏格达到这个上界的极化流形被称为Castelnuovo。 另一方面，一个格点多面体被称为Castelnuovo，如果其相关的极化环面簇是Castelnuovo。 Kawaguchi通过它们的$h^*$-向量来表征具有内部格点的Castelnuovo多面体。 在本文中，作为这一结果的推广，将给出所有Castelnuovo多面体的表征。 最后，作为我们表征的应用，我们给出了一个格点多面体为IDP的充分条件。 显示英文摘要

摘要： 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.