Algebraic properties of ideals of poset homomorphisms

Abstract

Given finite posets P and Q, we consider a specific ideal L(P, Q), whose minimal monomial generators correspond to order-preserving maps phi : P -> Q. We study algebraic invariants of those ideals. In particular, sharp lower and upper bounds for the Castelnuovo-Mumford regularity and the projective dimension are provided. We obtain precise formulas for a large subclass of these ideals. Moreover, we provide complete characterizations for several algebraic properties of L(P, Q), including being Buchsbaum, Cohen-Macaulay, Gorenstein, Golod and having a linear resolution.