Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Published electronically: September 7, 2017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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$).

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 13F55, 05E45

Retrieve articles in all journals with MSC (2010): 13F55, 05E45

Additional Information

Aldo Conca
Affiliation: DIMA – Dipartimento di Matematica, University of Genova, Via Dodecanesco 35, 16146 Genova, Italy

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

Volkmar Welker
Affiliation: Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans- Meerwein-Straße 6, 35032 Marburg, Germany

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

American Mathematical Society