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Motivic Milnor fiber of a quasi-ordinary hypersurface

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Published/Copyright: May 23, 2012
Journal für die reine und angewandte Mathematik (Crelles Journal)
From the journal Journal für die reine und angewandte Mathematik (Crelles Journal) Volume 2014 Issue 687

Abstract.

Let f:(𝐂d+1,0)→(𝐂,0) be a germ of complex analytic function such that its zero level defines an irreducible germ of quasi-ordinary hypersurface (S,0)⊂(𝐂d+1,0). We describe the motivic Igusa zeta function, the motivic Milnor fibre and the Hodge–Steenbrink spectrum of f at 0 in terms of topological invariants of (S,0)⊂(𝐂d+1,0).

Funding source: MCI-Spain

Award Identifier / Grant number: MTM2010-21740-C02

We are grateful to Nero Budur, Alejandro Melle Hernández and to András Némethi for several discussions and their useful suggestions concerning this paper. The second author is also grateful to Enrique Artal Bartolo, Mirel Căibar, Pierrette Cassou-Nogués, Gary Kennedy, Anatoly Libgober, Ignacio Luengo, Laurentiu Maxim, Lee McEwan and to the Alfred Renyi Institute of Mathematics (Hungary), the Department of Mathematics, Statistics and Computer Sciences of the University of Illinois at Chicago (USA) and Fundación Caja Madrid (Spain).

Received: 2011-02-22
Revised: 2012-04-13
Published Online: 2012-05-23
Published in Print: 2014-02-01

© 2014 by Walter de Gruyter Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Estimating the order of vanishing at infinity of Drinfeld quasi-modular forms
  3. Sharp weighted estimates for dyadic shifts and the A2 conjecture
  4. Non-integrability by discrete quadratures
  5. The cyclotomic polynomial topologically
  6. Projections of Richardson varieties
  7. Motivic Milnor fiber of a quasi-ordinary hypersurface
  8. The special values of Dirichlet L-functions as an analogue of the Iwasawa power series
  9. Valuations and surface area measures
https://doi.org/10.1515/crelle-2012-0049

Articles in the same Issue

  1. Frontmatter
  2. Estimating the order of vanishing at infinity of Drinfeld quasi-modular forms
  3. Sharp weighted estimates for dyadic shifts and the A2 conjecture
  4. Non-integrability by discrete quadratures
  5. The cyclotomic polynomial topologically
  6. Projections of Richardson varieties
  7. Motivic Milnor fiber of a quasi-ordinary hypersurface
  8. The special values of Dirichlet L-functions as an analogue of the Iwasawa power series
  9. Valuations and surface area measures
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