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Level algebras through Buchsbaum* manifolds. (English) Zbl 1231.13019

In the paper [“Buchsbaum* complexes”, arXiv:0909.1931], Chr. Athanasiadis and V. Welker introduced the notion of Buchsbaum* for a finite simplicial complex. This class includes all doubly Cohen-Macaulay complexes and all triangulations of orientable homology manifolds with boundary. I. Novik and E. Swartz [Adv. Math. 222, No. 6, 2059–2084 (2009; Zbl 1182.52010)] studied Buchsbaum complexes by investigating socles of Artinian reductions of their Stanley-Reisner rings. It yields a far reaching strengthening of the reviewer’s results on \(f\)-vectors of Buchsbaum complexes [Math. Z. 178, 125–142 (1981; Zbl 0472.13012)]. In the present paper the author extends the Novik-Swartz results to Buchsbaum* complexes. As an application the author establishes results on the enumeration of the faces of Buchsbaum* complexes improving those of Novik and Swartz [loc. cit.].

MSC:

13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
13H15 Multiplicity theory and related topics

Software:

BoijSoederberg
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References:

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