## Log-concavity of asymptotic multigraded Hilbert series

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- by Adam McCabe and Gregory G. Smith PDF
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**141**(2013), 1883-1892 Request permission

## 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.## References

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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
- MR Author ID: 622959
- Email: ggsmith@mast.queensu.ca
- Received by editor(s): September 20, 2011
- Published electronically: December 20, 2012
- Communicated by: Irena Peeva
- © Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**141**(2013), 1883-1892 - MSC (2010): Primary 05E40, 13D40, 52B20
- DOI: https://doi.org/10.1090/S0002-9939-2012-11808-8
- MathSciNet review: 3034415