Linear balls and the multiplicity conjecture

TL;DR

This paper studies linear balls and demonstrates that their boundary spheres' Stanley--Reisner rings satisfy the multiplicity conjecture, introducing a class of shellable spheres with this property.

Contribution

It introduces a class of shellable spheres derived from linear balls whose Stanley--Reisner rings satisfy the multiplicity conjecture, linking topology and algebra.

Findings

Stanley--Reisner rings of boundary spheres of linear balls satisfy the multiplicity conjecture

A new class of shellable spheres with this property is identified

The work connects geometric topology with algebraic properties of rings

Abstract

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.