The motivic Igusa zeta series of some hypersurfaces non-degenerated with respect to their Newton polyhedron
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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Department of Mathematics, City University of New York, USA United States
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