锥的投影与复曲面簇的算术秩
Projections of cones and the arithmetical rank of toric varieties
摘要：
设$I_M$和$I_N$是复曲面簇的定义理想，使得$I_M$是$I_N$的投影，即$I_N \subseteq I_M$。给出了等式$I_M=rad(I_N+(f_1,...,f_s))$成立的充要条件，其中$f_1,...,f_s$属于$I_M$ .给出了求集论完全交的复曲面簇的一种方法。最后，我们应用我们的方法计算某些复曲面簇的算术秩，并给出了上述复曲面簇的定义方程。
英文摘要：
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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