Projections of cones and the arithmetical rank of toric varieties

Details Projections of cones and the arithmetical rank of toric varieties Projections of cones and the arithmetical rank of toric varieties

2004-10-11

arxiv.org/abs/math/0410264v1

Mathematics

Commutative Algebra

To appear in the Journal of Pure and Applied Algebra

Scientific paper

Let $I_M$ and $I_N$ be defining ideals of toric varieties such that $I_M$ is a projection of $I_N$, i.e. $I_N \subseteq I_M$. We give necessary and sufficient conditions for the equality $I_M=rad(I_N+(f_1,...,f_s))$, where $f_1,...,f_s$ belong to $I_M$. Also a method for finding toric varieties which are set-theoretic complete intersection is given. Finally we apply our method in the computation of the arithmetical rank of certain toric varieties and provide the defining equations of the above toric varieties.

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