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arXiv · 1704.05601

On the $h$-vectors of the powers of graded ideals

Seyed Shahab Arkian·Amir Mafi
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Abstract

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.

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Seyed Shahab Arkian, Amir Mafi. 2017-04-19. On the $h$-vectors of the powers of graded ideals. https://arxiv.org/abs/1704.05601

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