Plane curves and their fundamental groups: Generalizations of Uludağ’s construction

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

References

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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

Volume 3, issue 1 (2003)

David Garber