Hokkaido Mathematical Journal

Bounds for the Betti numbers of successive stellar subdivisions of a simplex

Janko BÖHM and Stavros Argyrios PAPADAKIS

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We give a bound for the Betti numbers of the Stanley-Reisner ring of a stellar subdivision of a Gorenstein* simplicial complex by applying unprojection theory. From this we derive a bound for the Betti numbers of iterated stellar subdivisions of the boundary complex of a simplex. The bound depends only on the number of subdivisions, and we construct examples which prove that it is sharp.

Article information

Hokkaido Math. J., Volume 44, Number 3 (2015), 341-364.

First available in Project Euclid: 1 August 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13F55: Stanley-Reisner face rings; simplicial complexes [See also 55U10]
Secondary: 13D02: Syzygies, resolutions, complexes 13P20: Computational homological algebra [See also 13Dxx] 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]

Stanley-Reisner rings Betti numbers Resolutions Stellar subdivisions Simplices


BÖHM, Janko; PAPADAKIS, Stavros Argyrios. Bounds for the Betti numbers of successive stellar subdivisions of a simplex. Hokkaido Math. J. 44 (2015), no. 3, 341--364. doi:10.14492/hokmj/1470053368. https://projecteuclid.org/euclid.hokmj/1470053368

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