Some characterizations of special rings by delta-invariant

TL;DR

This paper explores characterizations of local rings being generically Gorenstein and Gorenstein using delta-invariant and linkage theory, providing new insights into their structural properties.

Contribution

It introduces novel characterizations of Gorenstein and generically Gorenstein rings via delta-invariant and linkage theory, expanding understanding of their algebraic structure.

Findings

Characterizations of Gorenstein rings using delta-invariant.

Criteria for generically Gorenstein rings based on linkage.

Connections between delta-invariant and ring properties.

Abstract

This paper is devoted to present some characterizations for a local ring to be generically Gorenstein and Gorenstein by means of $\delta$-invariant and linkage theory.