Linear balls and the multiplicity conjecture

A linear ball is a simplicial complex whose geometric realization is homeomorphic to a ball and whose Stanley-Reisner ring has a linear resolution. It turns out that the Stanley-Reisner ring of the sphere which is the boundary complex of a linear ball satisfies the multiplicity conjecture. A class of shellable spheres arising naturally from commutative algebra whose Stanley-Reisner rings satisfy the multiplicity conjecture will be presented. (C) 2008 Elsevier Inc. All rights reserved.