Singular cohomology of the analytic Milnor fiber, and mixed Hodge structure on the nearby cohomology

Nicaise, Johannes

doi:10.1090/S1056-3911-10-00526-6

Author: Johannes Nicaise
Journal: J. Algebraic Geom. 20 (2011), 199-237
DOI: https://doi.org/10.1090/S1056-3911-10-00526-6
Published electronically: January 21, 2010
MathSciNet review: 2762990
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Abstract | References | Additional Information

Abstract: We describe the homotopy type of the analytic Milnor fiber in terms of a strictly semi-stable model, and we show that its singular cohomology coincides with the weight zero part of the mixed Hodge structure on the nearby cohomology. We give a similar expression for Denef and Loeser’s motivic Milnor fiber in terms of a strictly semi-stable model.

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Additional Information

Johannes Nicaise
Affiliation: Université Lille 1, Laboratoire Painlevé, CNRS - UMR 8524, Cité Scientifique, 59655 Villeneuve d’Ascq Cédex, France
Address at time of publication: KULeuven, Department of Mathematics, Celestijnenlaan 200B, 3001 Heverlee, Belgium
MR Author ID: 725638
Email: johannes.nicaise@math.univ-lille1.fr, johannes.nicaise@wis.kuleuven.be

Received by editor(s): September 10, 2008
Received by editor(s) in revised form: January 21, 2009
Published electronically: January 21, 2010
Additional Notes: The research for this article was partially supported by ANR-06-BLAN-0183 and ANR-07-JCJC-0004