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Topology and combinatorics of real line arrangements

Published online by Cambridge University Press:  04 December 2007

Enrique Artal Bartolo ,
Jorge Carmona Ruber ,
José Ignacio Cogolludo Agustín  and
Miguel Marco Buzunáriz
Enrique Artal Bartolo
Affiliation:
Departamento de Matemáticas, Campus Plaza de San Francisco s/n, E-50009 Zaragoza, Spainartal@unizar.es
Jorge Carmona Ruber
Affiliation:
Departamento de Sistemas informáticos y programación, Universidad Complutense, Ciudad Universitaria s/n, E-28040 Madrid, Spainjcarmona@sip.ucm.es
José Ignacio Cogolludo Agustín
Affiliation:
Departamento de Matemáticas, Campus Plaza de San Francisco s/n, E-50009 Zaragoza, Spainjicogo@unizar.es
Miguel Marco Buzunáriz
Affiliation:
Departamento de Matemáticas, Campus Plaza de San Francisco s/n, E-50009 Zaragoza, Spainmmarco@unizar.es
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Abstract

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We prove the existence of complexified real arrangements with the same combinatorics but different embeddings in ${\mathbb P}^2$. Such a pair of arrangements has an additional property: they admit conjugated equations on the ring of polynomials over ${\mathbb Q}(\sqrt{5})$.

Keywords

line arrangementsbraid monodromy32S2214N2020F36 (primary)20E1832S5057M05 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 141 , Issue 6 , November 2005 , pp. 1578 - 1588
Copyright
Foundation Compositio Mathematica 2005