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Kummer covers and braid monodromy

Part of: Low-dimensional topology (Co)homology theory Curves Birational geometry

Published online by Cambridge University Press:  17 October 2013

Enrique Artal Bartolo ,
José Ignacio Cogolludo-Agustín  and
Jorge Ortigas-Galindo
Enrique Artal Bartolo
Affiliation:
Departamento de Matemáticas, IUMA, Universidad de Zaragoza, C. Pedro Cerbuna 12, 50009 Zaragoza, Spain ([email protected]; [email protected])
José Ignacio Cogolludo-Agustín
Affiliation:
Departamento de Matemáticas, IUMA, Universidad de Zaragoza, C. Pedro Cerbuna 12, 50009 Zaragoza, Spain ([email protected]; [email protected])
Jorge Ortigas-Galindo
Affiliation:
Centro Universitario de la Defensa-IUMA, Academia General Militar, Ctra. de Huesca s/n., 50090, Zaragoza, Spain ([email protected])
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Abstract

In this work, we describe a method to construct the generic braid monodromy of the preimage of a curve by a Kummer cover. This method is interesting since it combines two techniques, namely, the construction of a highly non-generic braid monodromy and a systematic method to go from a non-generic to a generic braid monodromy. The latter process, called generification, is independent from Kummer covers, and it can be applied in more general circumstances since non-generic braid monodromies appear more naturally and are oftentimes much easier to compute. Explicit examples are computed using these techniques.

Keywords

Kummer coversbraid monodromyplane curves

MSC classification

Secondary: 14H30: Coverings, fundamental group 14H50: Plane and space curves 57M12: Special coverings, e.g. branched 14E20: Coverings 14F45: Topological properties 14F35: Homotopy theory; fundamental groups
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 13 , Issue 3 , July 2014 , pp. 633 - 670
Copyright
©Cambridge University Press 2013 

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