抄録
In this article projective toric varieties are studied from the viewpoint of Gröbner basis theory and combinatorics. We characterize the radicals of all initial ideals of a toric variety X{\mathscr A} as the Stanley-Reisner ideals of regular triangulations of its set of weights {\mathscr A}. This implies that the secondary polytope Σ({\mathscr A}) is a Minkowski summand of the state polytope of X{\mathscr A}. Here the lexicographic (resp. reverse lexicographic) initial ideals of X{\mathscr A} arise from triangulations by placing (resp. pulling) vertices. We also prove that the state polytope of the Segre embedding of Pr-1×Ps-1 equals the secondary polytope Σ(Δr-1×Δs-1) of a product of simplices.
