Ralf Fröberg: Rings with (partly) linear resolution, mostly monomial rings

Abstract

I will define, discuss, and give examples of rings with \(d\)-linear resolution, and rings satisfying the condition \(N_p \,(N_{d,p})\), which means that the resolution is \(2\)-linear (\(d\)-linear) the first \(p\) times. Then I will concentrate on monomial rings, where of course more is known. I will, among other things, show an easy method to determine the Betti numbers of many monomial rings with 2-linear resolution. Finally I will also present some conjectures. This is mostly a survey talk, but some new results are given.