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.
Garber, David 1
@article{10_2140_agt_2003_3_593,
author = {Garber, David},
title = {Plane curves and their fundamental groups: {Generalizations} of {Uluda\u{g}{\textquoteright}s} construction},
journal = {Algebraic and Geometric Topology},
pages = {593--622},
year = {2003},
volume = {3},
number = {1},
doi = {10.2140/agt.2003.3.593},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2003.3.593/}
}
TY - JOUR AU - Garber, David TI - Plane curves and their fundamental groups: Generalizations of Uludağ’s construction JO - Algebraic and Geometric Topology PY - 2003 SP - 593 EP - 622 VL - 3 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2003.3.593/ DO - 10.2140/agt.2003.3.593 ID - 10_2140_agt_2003_3_593 ER -
%0 Journal Article %A Garber, David %T Plane curves and their fundamental groups: Generalizations of Uludağ’s construction %J Algebraic and Geometric Topology %D 2003 %P 593-622 %V 3 %N 1 %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2003.3.593/ %R 10.2140/agt.2003.3.593 %F 10_2140_agt_2003_3_593
Garber, David. Plane curves and their fundamental groups: Generalizations of Uludağ’s construction. Algebraic and Geometric Topology, Tome 3 (2003) no. 1, pp. 593-622. doi: 10.2140/agt.2003.3.593
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