The motivic Igusa zeta series of some hypersurfaces non-degenerated with respect to their Newton polyhedron

Hans Schoutens

Published: 2016-09-23

Vol. 30 (2016)

The motivic Igusa zeta series of some hypersurfaces non-degenerated with respect to their Newton polyhedron

Hans Schoutens

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.

Keywords:

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

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Schoutens, H. (2016). The motivic Igusa zeta series of some hypersurfaces non-degenerated with respect to their Newton polyhedron. Annales Mathematicae Silesianae, 30, 143–179. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13961

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Vol. 30 (2016)
Published: 2016-09-23

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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