Plane curves and their fundamental groups: Generalizations of Uludağ’s construction
| Autor: | David Garber |
|---|---|
| Rok vydání: | 2003 |
| Předmět: |
14H30
20F16 Pure mathematics 20F18 Group (mathematics) Plane curve plane curves Geometric Topology (math.GT) central extension Cyclic group Mathematics - Geometric Topology 14H30 20E22 20F16 20F18 Zariski pairs FOS: Mathematics Algebraic Topology (math.AT) Order (group theory) Mathematics - Algebraic Topology Geometry and Topology 20E22 Hirzebruch surfaces fundamental groups Mathematics |
| Zdroj: | Algebr. Geom. Topol. 3, no. 1 (2003), 593-622 |
| ISSN: | 1472-2739 1472-2747 |
| DOI: | 10.2140/agt.2003.3.593 |
| Popis: | 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. Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-21.abs.html |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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