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

Hans Schoutens — 2016

Annales Mathematicae Silesianae

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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