Betti numbers of Buchsbaum complexes. (English) Zbl 0727.55011

Björner, Anders; Hibi, Takayuki

Math. Scand. 67, No. 2, 193-196 (1990).

Summary: Given non-negative integers \(\beta_ 0,\beta_ 1,...,\beta_ d\) we construct a d-dimensional Buchsbaum complex \(\Delta\) over \({\mathbb{Z}}\) such that \(\tilde H_ i(\Delta;{\mathbb{Z}})\cong {\mathbb{Z}}^{\beta_ i}\) for all \(0\leq i\leq d\). This demonstrates (via work of P. Schenzel [Math. Z. 178, 125-142 (1981; Zbl 0472.13012)]) the existence of Stanley-Reisner rings with arbitrarily prescribed Betti numbers for local cohomology.

MSC:

55U10	Simplicial sets and complexes in algebraic topology
18G30	Simplicial sets; simplicial objects in a category (MSC2010)

Keywords:

Buchsbaum complex; Stanley-Reisner rings; Betti numbers; local cohomology