Resolutions of co-letterplace ideals and generalizations of Bier spheres

Abstract

We give the resolutions of co-letterplace ideals of posets in a completely explicit, very simple form. This generalizes and simplifies a number of linear resolutions in the literature, among them the Eliahou-Kervaire resolutions of strongly stable ideals generated in a single degree. Our method is based on a general result of K. Yanagawa using the canonical module of a Cohen-Macaulay Stanley-Reisner ring. We discuss in detail how the canonical module may effectively be computed, and from this derive directly the resolutions. A surprising consequence is that we obtain a large class of simplicial spheres comprehensively generalizing Bier spheres.