Resolutions of local face modules, functoriality, and vanishing of local $h$-vectors

Abstract

We study the local face modules of triangulations of simplices, i.e., the modules over face rings whose Hilbert functions are local $h$-vectors. In particular, we give resolutions of these modules by subcomplexes of Koszul complexes as well as functorial maps between modules induced by inclusions of faces. As applications, we prove a new monotonicity result for local $h$-vectors and new results on the structure of faces in triangulations with vanishing local $h$-vectors.

v2: 15 pages, minor improvements. To appear in Algebraic Combinatorics

References in corpus (3)

• The feasible region for consecutive patterns of permutations is a cycle polytope
• Triangulations of simplices with vanishing local h-polynomial
• Splitting groups with cubic Cayley graphs of connectivity two