Algebraic and Geometric Topology 3 (2003), paper no. 21, pages 593-622.

Plane curves and their fundamental groups: Generalizations of Uludag's construction

David Garber

Abstract. In this paper we investigate Uludag'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

AMS subject classification. Primary: 14H30. Secondary: 20E22,20F16,20F18.

DOI: 10.2140/agt.2003.3.593

E-print: arXiv:math.GT/0207131

Submitted: 23 January 2003. Accepted: 23 April 2003. Published: 22 June 2003.

Notes on file formats

David Garber
Institut Fourier, BP 74, 38402 Saint-Martin D'Heres CEDEX, FRANCE

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