On the geometry of complete intersection toric varieties

Details On the geometry of complete intersection toric varieties On the geometry of complete intersection toric varieties

2004-10-20

arxiv.org/abs/math/0410442v1

Mathematics

Algebraic Geometry

Scientific paper

In this paper we give a geometric characterization of the cones of toric varieties that are complete intersections. In particular, we prove that the class of complete intersection cones is the smallest class of cones which is closed under direct sum and contains all simplex cones. Further, we show that the number of the extreme rays of such a cone, which is less than or equal to $2n-2$, is exactly $2n-2$ if and only if the cone is a bipyramidal cone, where $n>1$ is the dimension of the cone. Finally, we characterize all toric varieties whose associated cones are complete intersection cones.

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