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2003 Plane curves and their fundamental groups: Generalizations of Uludağ's construction
David Garber
Algebr. Geom. Topol. 3(1): 593-622 (2003). DOI: 10.2140/agt.2003.3.593

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.

Citation

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David Garber. "Plane curves and their fundamental groups: Generalizations of Uludağ's construction." Algebr. Geom. Topol. 3 (1) 593 - 622, 2003. https://doi.org/10.2140/agt.2003.3.593

Information

Received: 23 January 2003; Revised: 27 February 2003; Accepted: 23 April 2003; Published: 2003
First available in Project Euclid: 21 December 2017

zbMATH: 1053.14027
MathSciNet: MR1997332
Digital Object Identifier: 10.2140/agt.2003.3.593

Subjects:
Primary: 14H30
Secondary: 20E22, 20F16, 20F18

Rights: Copyright © 2003 Mathematical Sciences Publishers

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