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Transactions of the American Mathematical Society

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

 
 

 

Resolutions of co-letterplace ideals and generalizations of Bier spheres


Authors: Alessio D’Alì, Gunnar Fløystad and Amin Nematbakhsh
Journal: Trans. Amer. Math. Soc. 371 (2019), 8733-8753
MSC (2010): Primary 13D02, 05E40; Secondary 52B55
DOI: https://doi.org/10.1090/tran/7560
Published electronically: March 28, 2019
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Abstract: We give the resolutions of co-letterplace ideals of posets in a completely explicit, very simple form. This generalizes and simplifies a number of linear resolutions in the literature, among them the Eliahou-Kervaire resolutions of strongly stable ideals generated in a single degree. Our method is based on a general result of K. Yanagawa using the canonical module of a Cohen-Macaulay Stanley-Reisner ring. We discuss in detail how the canonical module may effectively be computed and from this derive directly the resolutions.

A surprising consequence is that we obtain a large class of simplicial spheres comprehensively generalizing Bier spheres.


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Additional Information

Alessio D’Alì
Affiliation: Dipartimento di Matematica, Università degli Studi di Genova, Via Dodecaneso 35, 16146 Genova, Italy
Address at time of publication: Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
Email: alessio.d-ali@warwick.ac.uk

Gunnar Fløystad
Affiliation: Universitetet i Bergen, Matematisk institutt, Postboks 7803, 5020 Bergen, Norway
Email: gunnar@mi.uib.no

Amin Nematbakhsh
Affiliation: School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran
Email: nematbakhsh@ipm.ir

DOI: https://doi.org/10.1090/tran/7560
Received by editor(s): March 21, 2017
Received by editor(s) in revised form: January 11, 2018, February 13, 2018, and February 19, 2018
Published electronically: March 28, 2019
Additional Notes: Much of this work was carried out while the first and third authors were visiting the second author at the University of Bergen.
The third author received support from both the University of Bergen and the Institute for Research in Fundamental Sciences (IPM) during his stay.
Article copyright: © Copyright 2019 American Mathematical Society