Motivic Milnor Fibers of Plane Curve Singularities

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Abstract

We compute the motivic Milnor fiber of a complex plane curve singularity in an inductive and combinatoric way using the extended simplified resolution graph. The method introduced in this article has a consequence that one can study the Hodge–Steenbrink spectrum of such a singularity in terms of that of a quasi-homogeneous singularity.

Keywords

Plane curve singularity Newton polyhedron Resolution of singularity Extended resolution graph Arc spaces Motivic integration Motivic zeta function Motivic Milnor fiber 

Mathematics Subject Classification (2010)

Primary 14B05 14E15 14E18 14H20 14M25 32B30 32S55 

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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2017

Authors and Affiliations

  1. 1.Department of MathematicsVietnam National UniversityHanoiVietnam

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