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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Monodromy conjecture for nondegenerate surface singularities


Authors: Ann Lemahieu and Lise Van Proeyen
Journal: Trans. Amer. Math. Soc. 363 (2011), 4801-4829
MSC (2010): Primary 14B05
Published electronically: March 31, 2011
MathSciNet review: 2806692
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Abstract: We prove the monodromy conjecture for the topological zeta function for all nondegenerate surface singularities. Fundamental in our work is a detailed study of the formula for the zeta function of monodromy by Varchenko and the study of the candidate poles of the topological zeta function yielded by what we call `$ B_1$-facets'. In particular, new cases among the nondegenerate surface singularities for which the monodromy conjecture is now proven are the nonisolated singularities, the singularities giving rise to a topological zeta function with multiple candidate poles and the ones for which the Newton polyhedron contains a $ B_1$-facet.


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Additional Information

Ann Lemahieu
Affiliation: UFR de Mathématiques, Université Lille 1, 59655 Villeneuve d’Ascq, France
Email: lemahieu.ann@gmail.com

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

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05301-8
PII: S 0002-9947(2011)05301-8
Received by editor(s): November 9, 2009
Published electronically: March 31, 2011
Additional Notes: The first author’s research was partially supported by the Fund of Scientific Research - Flanders and MEC PN I+D+I MTM2007-64704.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.