<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

Publicado en línea: 23 sept 2016

Páginas: 143 - 179

Recibido: 14 abr 2016

Aceptado: 25 jun 2016

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

Palabras clave
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

Publicado en línea: 23 sept 2016

Páginas: 143 - 179

Recibido: 14 abr 2016

Aceptado: 25 jun 2016

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

Palabras clavemotivic 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.

Palabras clave
motivic Igusa zeta series, Du Val singularities, stationary phase method