On the type of an almost Gorenstein monomial curve

TL;DR

This paper investigates the Cohen-Macaulay type of almost Gorenstein monomial curves, establishing an upper bound of 3 for curves in four-dimensional affine space and discussing broader implications.

Contribution

It proves that the Cohen-Macaulay type of an almost Gorenstein monomial curve in 4 is at most 3, providing new bounds and insights into their algebraic structure.

Findings

Cohen-Macaulay type of such curves is at most 3

Results apply specifically to curves in 4

Discussion on general case considerations

Abstract

We prove that the Cohen-Macaulay type of an almost Gorenstein monomial curve $\mathcal C \subseteq \mathbb{A}^4$ is at most $3$, and make some considerations on the general case.