Seyed Shahab Arkian, Amir Mafi: On the h-vectors of the powers of graded ideals, 263-271

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 $k \gg0$, whenever $I$ is generated in a single degree.

Key Words: Hilbert series, Postulation number, regularity, Hilbert coefficients.

2010 Mathematics Subject Classification: Primary 13D40, 13C15, 13D07; Secondary 13D02.