Golod ideals in combinatorial commutative algebra

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.