The Golod property for products and high symbolic powers of monomial ideals

TL;DR

This paper proves that the quotient rings formed by products and high symbolic powers of monomial ideals are Golod, with implications for the cohomology of certain topological spaces, advancing understanding in algebraic and topological properties.

Contribution

It establishes the Golod property for products of monomial ideals and for large symbolic powers, providing new insights into their algebraic structure.

Findings

S/IJ is Golod for any monomial ideals I, J

S/I^{(k)} is Golod for large k when I is squarefree

Trivial multiplication in cohomology of certain moment-angle complexes

Abstract

We show that for any two proper monomial ideals I and J in the polynomial ring S = k[x_1, ..., x_n] the ring S/IJ is Golod. We also show that if I is squarefree then for large enough k the quotient S/I^{(k)} of S by the kth symbolic power of I is Golod. As an application we prove that the multiplication on the cohomology algebra of some classes of moment-angle complexes is trivial.