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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Plane curves and their fundamental groups: Generalizations of Uludağ's construction

David Garber

Algebraic & Geometric Topology 3 (2003) 593–622

arXiv: math.GT/0207131

Abstract

In this paper we investigate Uludağ’s method for constructing new curves whose fundamental groups are central extensions of the fundamental group of the original curve by finite cyclic groups.

In the first part, we give some generalizations to his method in order to get new families of curves with controlled fundamental groups. In the second part, we discuss some properties of groups which are preserved by these methods. Afterwards, we describe precisely the families of curves which can be obtained by applying the generalized methods to several types of plane curves. We also give an application of the general methods for constructing new Zariski pairs.

Keywords
fundamental groups, plane curves, Zariski pairs, Hirzebruch surfaces, central extension
Mathematical Subject Classification 2000
Primary: 14H30
Secondary: 20E22, 20F16, 20F18
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Publication
Received: 23 January 2003
Revised: 27 February 2003
Accepted: 23 April 2003
Published: 22 June 2003
Authors
David Garber
Institut Fourier
BP 74
38402 Saint-Martin D’Heres CEDEX
FRANCE