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arXiv · 1703.06460

Almost Buchsbaumness of some rings arising from complexes with isolated singularities

Connor Sawaske
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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.

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Connor Sawaske. 2017-03-19. Almost Buchsbaumness of some rings arising from complexes with isolated singularities. https://arxiv.org/abs/1703.06460

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