Golod ideals in combinatorial commutative algebra

TL;DR

This paper investigates the Golod property in standard graded algebras, providing characterizations for various classes such as determinantal, binomial edge, and cover ideals, and establishing new conditions for strongly Golod ideals.

Contribution

It offers new characterizations of Golod ideals in combinatorial algebra, including criteria for determinantal, binomial edge, and cover ideals, and extends results to strongly Golod ideals.

Findings

Determinantal, binomial edge, and permanental ideals are Golod iff they have a linear resolution.

Cover ideals define Golod rings under specific multidegree conditions.

Squarefree strongly Golod ideals are proven to be Golod, not just weakly Golod.

Abstract

In this article we study the Golod property of standard graded algebras. We show that determinantal ideals, binomial edge ideals, and permanental ideals are Golod if and only if they have a linear resolution. Next, we give a characterization of when cover ideals define Golod rings, exploiting some considerations on multidegrees of Koszul cycles and Massey products. Finally, we show that squarefree strongly Golod ideals (and, more generally, lcm-strongly Golod ideals) are Golod, and not just weakly Golod.