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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Log-concavity of asymptotic multigraded Hilbert series


Authors: Adam McCabe and Gregory G. Smith
Journal: Proc. Amer. Math. Soc. 141 (2013), 1883-1892
MSC (2010): Primary 05E40, 13D40, 52B20
Published electronically: December 20, 2012
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Abstract | References | Similar Articles | Additional Information

Abstract: We study the linear map sending the numerator of the rational function representing the Hilbert series of a module to that of its $ r$-th Veronese submodule. We show that the asymptotic behaviour as $ r$ tends to infinity depends on the multidegree of the module and the underlying positively multigraded polynomial ring. More importantly, we give a polyhedral description for the asymptotic polynomial and prove that the coefficients are log-concave.


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Additional Information

Adam McCabe
Affiliation: 35 Summerhill Road, Holland Landing, Ontario, L9N 1C6, Canada
Email: adam.r.mccabe@gmail.com

Gregory G. Smith
Affiliation: Department of Mathematics & Statistics, Queen’s University, Kingston, Ontario, K7L 3N6, Canada
Email: ggsmith@mast.queensu.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11808-8
PII: S 0002-9939(2012)11808-8
Received by editor(s): September 20, 2011
Published electronically: December 20, 2012
Communicated by: Irena Peeva
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.