边界的希尔伯特函数的一组点在P^{n_1} x. x P^{n_k}
The border of the Hilbert function of a set of points in P^{n_1} x ... x P^{n_k}
摘要：
我们描述的最终行为的希尔伯特函数的一组不同的点在P^{n_1} x. x P^{n_k}。作为这一结果的后果，我们表明，在P^{n_1} x的一组点的希尔伯特函数. x P^{n_k}可以通过仅在有限个值处计算希尔伯特函数来确定。我们的结果推广了P^n中点集的Hilbert函数稳定于点集的基数的结果。在此基础上，我们引入了点集的Hilbert函数的边界的概念。利用Gale-Ryser定理，刻画了P^1 × P^1中不同点集上Hilbert函数的所有可能边界.
英文摘要：
We describe the eventual behaviour of the Hilbert function of a set of distinct points in P^{n_1} x ... x P^{n_k}. As a consequence of this result, we show that the Hilbert function of a set of points in P^{n_1} x ... x P^{n_k} can be determined by computing the Hilbert function at only a finite number of values. Our result extends the result that the Hilbert function of a set of points in P^n stabilizes at the cardinality of the set of points. Motivated by our result, we introduce the notion of the_border_ of the Hilbert function of a set of points. By using the Gale-Ryser Theorem, a classical result about (0,1)-matrices, we characterize all the possible borders for the Hilbert function of a set of distinct points in P^1 x P^1.
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