The Motivic Igusa Zeta Series of Some Hypersurfaces Non-Degenerated with Respect to their Newton Polyhedron

Hans Schoutens

doi:10.1515/amsil-2016-0010

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The Motivic Igusa Zeta Series of Some Hypersurfaces Non-Degenerated with Respect to their Newton Polyhedron

Annales Mathematicae Silesianae

Volume 30 (2016): Issue 1 (September 2016)

By: Hans Schoutens

Open Access

|Sep 2016

Abstract

We describe some algorithms, without using resolution of singularities, that establish the rationality of the motivic Igusa zeta series of certain hypersurfaces that are non-degenerated with respect to their Newton polyhedron. This includes, in any characteristic, the motivic rationality for polydiagonal hypersurfaces, vertex singularities, binomial hypersurfaces, and Du Val singularities.

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Articles in this issue

DOI: https://doi.org/10.1515/amsil-2016-0010 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 143 - 179

Submitted on: Apr 14, 2016

Accepted on: Jun 25, 2016

Published on: Sep 23, 2016

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

motivic Igusa zeta series,

Du Val singularities,

stationary phase method

Related subjects:

Mathematics,

General mathematics

© 2016 Hans Schoutens, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 30 (2016): Issue 1 (September 2016)