15 March 2003 The Alexander polynomial of a plane curve singularity via the ring of functions on it
A. Campillo, F. Delgado, S. M. Gusein-Zade
Duke Math. J. 117(1): 125-156 (15 March 2003). DOI: 10.1215/S0012-7094-03-11712-3

Abstract

We prove two formulae that express the Alexander polynomial $\Delta\sp C$ of several variables of a plane curve singularity $C$ in terms of the ring $\mathscr {O}\sb C$ of germs of analytic functions on the curve. One of them expresses $\Delta\sp C$ in terms of dimensions of some factors corresponding to a (multi-indexed) filtration on the ring $\mathscr {O}\sb C$. The other one gives the coefficients of the Alexander polynomial $\Delta\sp C$ as Euler characteristics of some explicitly described spaces (complements to arrangements of projective hyperplanes).

Citation

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A. Campillo. F. Delgado. S. M. Gusein-Zade. "The Alexander polynomial of a plane curve singularity via the ring of functions on it." Duke Math. J. 117 (1) 125 - 156, 15 March 2003. https://doi.org/10.1215/S0012-7094-03-11712-3

Information

Published: 15 March 2003
First available in Project Euclid: 26 May 2004

zbMATH: 1028.32013
MathSciNet: MR1962784
Digital Object Identifier: 10.1215/S0012-7094-03-11712-3

Subjects:
Primary: 14H20
Secondary: 32Sxx

Rights: Copyright © 2003 Duke University Press

Vol.117 • No. 1 • 15 March 2003
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