Grobner bases of toric varieties
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概要
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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 P<SUP>r-1</SUP>×P<SUP>s-1</SUP> equals the secondary polytope Σ(Δ<SUB>r-1</SUB>×Δ<SUB>s-1</SUB>) of a product of simplices.
- 東北大学の論文
- 1991-06-00