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
Email: garber@mozart.ujf-grenoble.fr
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