Level algebras through Buchsbaum* manifolds

TL;DR

This paper investigates Stanley-Reisner rings of Buchsbaum* complexes, computes their socles, and demonstrates that certain quotients are level algebras, leading to new face vector restrictions.

Contribution

It extends recent results to Buchsbaum* complexes, showing their quotients are level algebras after socle reduction, providing new combinatorial restrictions.

Findings

Socle of quotients computed

Quotients modulo socle are level algebras

New face vector restrictions for Buchsbaum* complexes

Abstract

Stanley-Reisner rings of Buchsbaum* complexes are studied by means of their quotients modulo a linear system of parameters. The socle of these quotients is computed. Extending a recent result by Novik and Swartz for orientable homology manifolds without boundary, it is shown that modulo a part of their socle these quotients are level algebras. This provides new restrictions on the face vectors of Buchsbaum* complexes.