On the Vanishing of the normal Hilbert coefficients of ideals

TL;DR

This paper establishes bounds on the normal reduction number of ideals in Cohen-Macaulay local rings by analyzing the vanishing of graded components of local cohomology modules, linking it to the vanishing of normal Hilbert coefficients.

Contribution

It provides new bounds and conditions relating the vanishing of normal Hilbert coefficients to the normal reduction number in Cohen-Macaulay rings.

Findings

Bounds on the normal reduction number derived from local cohomology vanishing

Necessary and sufficient conditions for vanishing of normal Hilbert coefficients

Characterization in Cohen-Macaulay local rings of dimension ≥ 3

Abstract

Using vanishing of graded components of local cohomology modules of the Rees algebra of the normal filtration of an ideal, we give bounds on the normal reduction number. This helps to get necessary and sufficient conditions in Cohen-Macaulay local rings of dimension $d\geq 3$, for the vanishing of the normal Hilbert coefficients $\overline{e}_k(I)$ for $k\leq d,$ in terms of the normal reduction number.