Abstract:

Golodness of a Stanley-Reisner ring $k[\Delta]$ over a field $k$ has not yet been fully characterized in terms of the combinatorics of the simplicial complex $\Delta$. It has been proved by Herzog, Reiner and Welker that if the Alexander dual $\Delta^\vee$ is sequentially Cohen-Macaulay over $k$ then $k[\Delta]$ is Golod, but the converse is false.

In this talk, we will introduce a combinatorial condition on a simplicial complex, called the strong gcd-condition, that implies Golodness of the associated Stanley-Reisner ring. The condition is reminiscent of shellability, and in fact one can show that if $\Delta^\vee$ is (non-pure) shellable then $\Delta$ satisfies the strong gcd-condition. For flag complexes, the strong gcd-condition turns out to be equivalent to Golodness.

This is joint work with Michael Jöllenbeck.