On the relation between formal grade and depth with a view toward vanishing of Lyubeznik numbers

TL;DR

This paper explores the relationship between formal grade and depth in local rings and investigates conditions under which Lyubeznik numbers vanish, contributing to the understanding of local cohomology invariants.

Contribution

It advances the comparison between formal grade and depth, and provides new results on the vanishing of Lyubeznik numbers in local rings.

Findings

Established new inequalities relating formal grade and depth.

Derived conditions for the vanishing of Lyubeznik numbers.

Extended previous results on local cohomology invariants.

Abstract

Let $(R,\fm)$ be a local ring and $I$ an ideal. The aim of the present paper is twofold. At first we continue the investigation to compare $\fgrade(I,R)$ with $\depth R/I$ and further we derive some results on the vanishing of Lyubeznik numbers.