THE ALEXANDER POLYNOMIAL OF A PLANE CURVE SINGULARITY AND INTEGRALS WITH RESPECT TO THE EULER CHARACTERISTIC-Reference-Cited by-同舟云学术

THE ALEXANDER POLYNOMIAL OF A PLANE CURVE SINGULARITY AND INTEGRALS WITH RESPECT TO THE EULER CHARACTERISTIC

Published:2003-02 Issue:01 Volume:14 Page:47-54
ISSN:0129-167X
Container-title:International Journal of Mathematics
language:en
Short-container-title:Int. J. Math.

Author:

CAMPILLO A.¹,DELGADO F.¹,GUSEIN-ZADE S. M.²

Affiliation:

1. University of Valladolid, Department of Algebra, Geometry and Topology, 47005 Valladolid, Spain

2. Moscow State University, Faculty of Mathematics and Mechanics, Moscow, 119899, Russia

Abstract

It was shown that the Alexander polynomial (of several variables) of a (reducible) plane curve singularity coincides with the (generalized) Poincaré polynomial of the multi-indexed filtration defined by the curve on the ring [Formula: see text] of germs of functions of two variables. The initial proof of the result was rather complicated (it used analytical, topological and combinatorial arguments). Here we give a new proof based on the notion of the integral with respect to the Euler characteristic over the projectivization of the space [Formula: see text] — the notion similar to (and inspired by) the notion of the motivic integration.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129167X03001703

Reference6 articles.

1. Germs of arcs on singular algebraic varieties and motivic integration

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