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.