<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

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

Department of Mathematics, City University of New York, 365 Fifth Avenue, New York, NY 10016,

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

We describe some algorithms, without using resolution of singularities, that establish the rationality of the motivic Igusa zeta series of certain...

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

Published Online: Sep 23, 2016

Page range: 143 - 179

Received: Apr 14, 2016

Accepted: Jun 25, 2016

DOI: https://doi.org/10.1515/amsil-2016-0010

Keywords
motivic Igusa zeta series, Du Val singularities, stationary phase method

© 2016 Hans Schoutens, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Sep 23, 2016

Page range: 143 - 179

Received: Apr 14, 2016

Accepted: Jun 25, 2016

DOI: https://doi.org/10.1515/amsil-2016-0010

Keywordsmotivic Igusa zeta series, Du Val singularities, stationary phase method

© 2016 Hans Schoutens, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
motivic Igusa zeta series, Du Val singularities, stationary phase method