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FUNDAMENTAL GROUP FOR SOME CUSPIDAL CURVES

Published online by Cambridge University Press:  01 March 1999

JOSÉ IGNACIO COGOLLUDO
JOSÉ IGNACIO COGOLLUDO
Affiliation:
Departamento de Álgebra, Universidad Complutense de Madrid, Av. Ciudad Universitaria s/n, 28040 Madrid, Spain Current address: Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 S. Morgan Street, Chicago, IL 60607-7045, USA.
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Abstract

In [1], Hirano gives a method for constructing families of curves with a large number of singularities. The idea is to consider an abelian covering of ℙ2 ramified along three lines in general position, and to take the pull-back of a curve C intersecting the lines non-generically. Similar constructions are used by Shimada in [10] and Oka in [8]. We apply this method for the case where C is a conic, constructing a family of curves with the following asymptotic behaviour (see [9]):

formula here

The goal of this paper is to calculate the fundamental group for the curves in this family as well as their Alexander polynomial.

Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 31 , Issue 2 , March 1999 , pp. 136 - 142
Copyright
© The London Mathematical Society 1999

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