# Almost Buchsbaumness of some rings arising from complexes with isolated singularities

## TL;DR

This paper investigates the algebraic properties of Stanley-Reisner rings derived from simplicial complexes with isolated singularities, focusing on their behavior when reduced modulo two generic linear forms, revealing cases that are quasi-Buchsbaum but not Buchsbaum.

## Contribution

It extends previous work by analyzing complexes with non-homologically isolated singularities, showing that their associated rings can be quasi-Buchsbaum rather than Buchsbaum.

## Key findings

- Many examples of quasi-Buchsbaum rings obtained by modulo two forms
- Identification of non-homologically isolated singularities leading to quasi-Buchsbaum rings
- Extension of Buchsbaum property analysis to more general singularity cases

## Abstract

We study properties of the Stanley-Reisner rings of simplicial complexes with isolated singularities modulo two generic linear forms. Miller, Novik, and Swartz proved that if a complex has homologically isolated singularities, then its Stanley-Reisner ring modulo one generic linear form is Buchsbaum. Here we examine the case of non-homologically isolated singularities, providing many examples in which the Stanley-Reisner ring modulo two generic linear forms is a quasi-Buchsbaum but not Buchsbaum ring.