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Computation-free presentation of the fundamental group of generic (p,q)–torus curves

Enrique Artal Bartolo, José Ignacio Cogolludo Agustín and Jorge Ortigas-Galindo

Algebraic & Geometric Topology 12 (2012) 1265–1272

DOI: 10.2140/agt.2012.12.1265
Abstract

We present a new method for computing fundamental groups of curve complements using a variation of the Zariski–van Kampen method on general ruled surfaces. As an application we give an alternative (computation-free) proof for the fundamental group of generic (p,q)–torus curves.

Keywords

algebraic curve, fundamental group, braid monodromy
Mathematical Subject Classification

Primary: 14F45, 14H30, 14H50

Secondary: 14E05, 14H10, 57M05, 57M12
References
Publication

Received: 16 January 2012
Revised: 23 March 2012
Accepted: 28 March 2012
Published: 9 June 2012
Authors
Enrique Artal Bartolo
Departamento de Matemáticas, IUMA
Universidad de Zaragoza
C/ Pedro Cerbuna 12
50009 Zaragoza
Spain
http://riemann.unizar.es/geotop/WebGeoTo/Profes/eartal/
José Ignacio Cogolludo Agustín
Departamento de Matemáticas, IUMA
Universidad de Zaragoza
C/ Pedro Cerbuna 12
50009 Zaragoza
Spain
http://riemann.unizar.es/~jicogo/
Jorge Ortigas-Galindo
Centro Universitario de la Defensa-IUMA
Universidad de Zaragoza
Academia General Militar
Ctra de Huesca s/n
50090 Zaragoza
Spain
http://riemann.unizar.es/~jortigas/