Monodromy conjecture for nondegenerate surface singularities
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- by Ann Lemahieu and Lise Van Proeyen PDF
- Trans. Amer. Math. Soc. 363 (2011), 4801-4829 Request permission
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.References
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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
- 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.
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 363 (2011), 4801-4829
- MSC (2010): Primary 14B05
- DOI: https://doi.org/10.1090/S0002-9947-2011-05301-8
- MathSciNet review: 2806692