Vanishing of local cohomology and set-theoretically Cohen-Macaulay ideals

TL;DR

This paper explores the relationship between local cohomology and set-theoretically Cohen-Macaulay ideals, providing new cohomological characterizations and generalizations of existing results in algebraic geometry.

Contribution

It introduces new cohomological criteria for identifying set-theoretically Cohen-Macaulay ideals and generalizes known results linking cohomological and projective dimensions.

Findings

Established new cohomological characterizations of set-theoretically Cohen-Macaulay ideals

Generalized known results on the relation between cohomological and projective dimension

Provided theoretical insights into local cohomology vanishing conditions

Abstract

We generalize some known results on the relation between the cohomological and projective dimension. Then we examine the set-theoretically Cohen-Macaulay ideals to find some cohomological characterization of these kind of ideals.