The Hilbert function of a maximal Cohen-Macaulay module Part II

TL;DR

This paper proves that the Hilbert function of a maximal Cohen-Macaulay module over certain complete intersections is non-decreasing, extending the result to codimension two cases, providing insights into module behavior over these rings.

Contribution

It establishes the non-decreasing property of the Hilbert function for maximal Cohen-Macaulay modules over strict complete intersections and codimension two cases, advancing understanding of their algebraic structure.

Findings

Hilbert function of M is non-decreasing over strict complete intersections.

The non-decreasing property also holds for complete intersections of codimension two.

Provides new results on the behavior of maximal Cohen-Macaulay modules.

Abstract

Let $(A,\m)$ be a strict complete intersection of positive dimension and let $M$ be a maximal \CM \ $A$-module with bounded betti-numbers. We prove that the Hilbert function of $M$ is non-decreasing. We also prove an analogous statement for complete intersections of codimension two.