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

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

2002-07-16

arxiv.org/abs/math/0207131v5

Algebr. Geom. Topol. 3 (2003) 593-622

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-21.abs.html

Scientific paper

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.

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