The Bi-Canonical Degree of a Cohen-Macaulay Ring

TL;DR

This paper introduces the bi-canonical degree, a new invariant for Cohen-Macaulay rings with canonical ideals, providing a uniform framework and computational insights to characterize specific ring classes.

Contribution

It defines the bi-canonical degree, extending the canonical degree, and explores its properties and computational aspects for Cohen-Macaulay rings.

Findings

Minimal bi-canonical degree characterizes specific Cohen-Macaulay classes

Provides a uniform presentation of the bi-canonical degree

Discusses computational methods for the bi-canonical degree

Abstract

This paper is a sequel to [8] where we introduced an invariant, called canonical degree, of Cohen-Macaulay local rings that admit a canonical ideal. Here to each such ring with a canonical ideal, we attach a different invariant, called bi-canonical degree, which in dimension 1 appears also in [12] as the residue of a ring. The minimal values of these functions characterize specific classes of Cohen-Macaulay rings. We give a uniform presentation of such degrees and discuss some computational opportunities offered by the bi-canonical degree.