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On complex line arrangements and their boundary manifolds

Published online by Cambridge University Press:  25 May 2015

V. FLORENS ,
B. GUERVILLE-BALLÉ  and
M.A. MARCO-BUZUNARIZ
V. FLORENS
Affiliation:
LMA, UMR CNRS 5142, Université de Pau et des Pays de l'Adour, 64000 Pau, France. e-mail: vincent.florens@univ-pau.fr
B. GUERVILLE-BALLÉ
Affiliation:
IJF, UMR 5582 CNRS-UJF, Université Grenoble Alpes, 38 000 Grenoble, France. e-mail: benoit.guerville-balle@math.cnrs.fr
M.A. MARCO-BUZUNARIZ
Affiliation:
ICMAT: CSIC-Complutense-Autonoma-Carlos III, Departamento de Algebra, Facultad de CC. Matematicas - Plaza de las Ciencias, 3, 28040 Madrid, Spain. e-mail: mmarco@unizar.es
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Abstract

Let ${\mathcal A}$ be a line arrangement in the complex projective plane $\mathds{C}\mathds{P}^2$. We define and describe the inclusion map of the boundary manifold, the boundary of a closed regular neighbourhood of ${\mathcal A}$, in the exterior of the arrangement. We obtain two explicit descriptions of the map induced on the fundamental groups. These computations provide a new minimal presentation of the fundamental group of the complement.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 159 , Issue 2 , September 2015 , pp. 189 - 205
Copyright
Copyright © Cambridge Philosophical Society 2015 

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References

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