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On the $h$-vectors of the powers of graded ideals. (arXiv:1704.05601v2 [math.AG] UPDATED)

来源于:arXiv
Let $S=K[x_1,\ldots,x_n]$ be the polynomial ring over the field $K$, and let $I\subset S$ be a graded ideal. It is shown that for $k \gg0$ the postulation number of $I^k$ is bounded by a linear function of $k$, and it is a linear function of $k$, if $I$ is generated in a single degree. By using the relationship of the $h$-vector with the higher iterated Hilbert coefficients of $I^k$ it is shown that the Hilbert coefficients $e_i(I^k)$ of $I^k$ are polynomials for $k \gg 0$, whenever $I$ is generated in a single degree. 查看全文>>