Betti numbers of monomial ideals via facet covers

Abstract

We give a sufficient condition for a monomial ideal to have a nonzero Betti number in each multidegree. In the case of facet ideals of simplicial forests, this condition becomes a necessary one and it allows us to characterize Betti numbers, projective dimension and regularity of such ideals combinatorially. Our condition is expressed in terms of minimal facet covers of simplicial complexes.

References in corpus (3)

• Matchings, coverings, and Castelnuovo-Mumford regularity
• Boij-Söderberg theory: Introduction and survey
• Edge ideals: algebraic and combinatorial properties

Cited by in corpus (2)

• Projective dimension and regularity of edge ideals of some vertex-weighted oriented $m$-partite graphs
• Projective dimension and regularity of powers of edge ideals of vertex-weighted rooted forests