Resolutions of co-letterplace ideals and generalizations of Bier spheres

TL;DR

This paper provides explicit resolutions for co-letterplace ideals of posets, generalizing known resolutions and leading to a broad class of simplicial spheres that extend Bier spheres.

Contribution

It introduces a simple, explicit method for resolving co-letterplace ideals, generalizing several existing linear resolutions and connecting to the canonical module of Cohen-Macaulay rings.

Findings

Explicit resolutions of co-letterplace ideals derived

Generalization of Bier spheres achieved

Method based on canonical modules of Stanley-Reisner rings

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.