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Almost Buchsbaumness of some rings arising from complexes with isolated singularities. (English) Zbl 1452.13029
Author’s abstract: We study properties of the Stanley-Reisner rings of simplicial complexes with isolated singularities modulo two generic linear forms. Miller, Novik, and Swartz [E. Miller et al., Math. Ann. 351, No. 4, 857–875 (2011; Zbl 1236.13017)] 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.
MSC:
13F55 Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
13D45 Local cohomology and commutative rings
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