Cellular Resolutions of Ideals Defined by Simplicial Homomorphisms

摘要

In this paper we introduce the class of ordered homomorphism ideals and provethat these ideals admit minimal cellular resolutions constructed ashomomorphism complexes. As a key ingredient of our work, we introduce the classof cointerval simplicial complexes and investigate their combinatorial andtopological properties. As a concrete illustration of these structural results,we introduce and study nonnesting monomial ideals, an interesting family ofcombinatorially defined ideals.