- Akiyoshi Tsuchiya (University of Tokyo, Meguro-ku, Japan)
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, there is a one-to-one correspondence between full-dimensional lattice polytopes and polarized toric varieties and we call a lattice polytope Castelnuovo if the associated polarized toric variety is Castelnuovo. In this talk, I give a combinatorial characterization of Castelnuovo polytopes and an application of this characterization.