Depth Sensitivity of Hilbert Coefficients

2025/04/28 by Koji Nishida, Nishida, Koji
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Polynomial and algebraic computation #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2504.19597

Abstract

The purpose of this paper is to explain about the depth sensitivity of the Hilbert coefficients defined for finitely generated graded modules over graded rings. The main result generalize the well known fact that the Cohen-Macaulayness of graded modules can be characterized using their multiplicities.

Related

• Hilbert coefficients and depths of form rings
• Hilbert Coefficients and Depth of the Associated Graded Ring of an Ideal
• An algorithm to compute the Hilbert depth
• Hilbert depth of graded modules over polynomial rings in two variables
• Depth of associated graded rings via Hilbert coefficients of ideals