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 nonhomologically isolated singularities, providing many examples in which the Stanley–Reisner ring modulo two generic linear forms is a quasi-Buchsbaum but not Buchsbaum ring.
"Almost Buchsbaumness of some rings arising from complexes with isolated singularities." J. Commut. Algebra 12 (1) 115 - 133, Spring 2020. https://doi.org/10.1216/jca.2020.12.115