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The holomorphy conjecture for ideals in dimension two


Authors: Ann Lemahieu and Lise Van Proeyen
Journal: Proc. Amer. Math. Soc. 139 (2011), 3845-3852
MSC (2010): Primary 14-XX
DOI: https://doi.org/10.1090/S0002-9939-2011-11186-9
Published electronically: June 29, 2011
MathSciNet review: 2823031
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Abstract: The holomorphy conjecture predicts that the topological zeta function associated to a polynomial $ f \in \mathbb{C}[x_1,\ldots,x_n]$ and an integer $ d > 0$ is holomorphic unless $ d$ divides the order of an eigenvalue of local monodromy of $ f$. In this paper, we generalise the holomorphy conjecture to the setting of arbitrary ideals in $ \mathbb{C}[x_1,\ldots,x_n]$, and we prove it when $ n=2$.


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Additional Information

Ann Lemahieu
Affiliation: Departement Wiskunde, K. U. Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
Address at time of publication: Université Lille 1, UFR de Mathématiques, Cité Scientifique, 59655 Villeneuve d’Ascq Cedex, France
Email: lemahieu.ann@gmail.com

Lise Van Proeyen
Affiliation: Departement Wiskunde, K. U. Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
Email: lisevanproeyen@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2011-11186-9
Received by editor(s): May 16, 2008
Received by editor(s) in revised form: May 6, 2009, and September 18, 2010
Published electronically: June 29, 2011
Additional Notes: This research was partially supported by the Fund of Scientific Research - Flanders (G.0318.06) and MEC PN I+D+I MTM2007-64704.
Communicated by: Ted Chinburg
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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