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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Asymptotic syzygies of Stanley-Reisner rings of iterated subdivisions


Authors: Aldo Conca, Martina Juhnke-Kubitzke and Volkmar Welker
Journal: Trans. Amer. Math. Soc. 370 (2018), 1661-1691
MSC (2010): Primary 13F55, 05E45
DOI: https://doi.org/10.1090/tran/7149
Published electronically: September 7, 2017
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Abstract: Inspired by recent results of Ein, Lazarsfeld, Erman and Zhou on the non-vanishing of Betti numbers of high Veronese subrings, we describe the behavior of the Betti numbers of Stanley-Reisner rings associated with iterated barycentric or edgewise subdivisions of a given simplicial complex. Our results show that for a simplicial complex $ \Delta $ of dimension $ d-1$ and for $ 1\leq j\leq d-1$ the number of 0's in the $ j^{\text {th}}$ linear strand of the minimal free resolution of the $ r^{\text {th}}$ barycentric or edgewise subdivision is bounded above only in terms of $ d$ and $ j$ (and independently of $ r$).


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Aldo Conca
Affiliation: DIMA – Dipartimento di Matematica, University of Genova, Via Dodecanesco 35, 16146 Genova, Italy
Email: conca@dima.unige.it

Martina Juhnke-Kubitzke
Affiliation: Fachbereich Informatik und Mathematik, Goethe-Universität Frankfurt, Postfach 11 19 32, D-60054 Frankfurt am Main, Germany
Address at time of publication: Institut für Mathematik, Universität Osnabrück, Albrechtstraße 28a, 49076 Osnabrück, Germany
Email: juhnke-kubitzke@uos.de

Volkmar Welker
Affiliation: Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans- Meerwein-Straße 6, 35032 Marburg, Germany
Email: welker@mathematik.uni-marburg.de

DOI: https://doi.org/10.1090/tran/7149
Keywords: Betti numbers, subdivision, Stanley-Reisner ring
Received by editor(s): November 30, 2015
Received by editor(s) in revised form: May 23, 2016
Published electronically: September 7, 2017
Article copyright: © Copyright 2017 American Mathematical Society

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