61505 20191113135212.0 doi 10.1007/s13398-016-0298-y sideral 98429 ART-2017-98429 eng (orcid)0000-0002-8276-5116 Artal Bartolo, E. Universidad de Zaragoza An arithmetic Zariski pair of line arrangements with non-isomorphic fundamental group 2017 Access copy available to the general public Unrestricted In a previous work, the third named author found a combinatorics of line arrangements whose realizations live in the cyclotomic group of the fifth roots of unity and such that their non-complex-conjugate embedding are not topologically equivalent in the sense that they are not embedded in the same way in the complex projective plane. That work does not imply that the complements of the arrangements are not homeomorphic. In this work we prove that the fundamental groups of the complements are not isomorphic. It provides the first example of a pair of Galois-conjugate plane curves such that the fundamental groups of their complements are not isomorphic (despite the fact that they have isomorphic profinite completions). info:eu-repo/grantAgreement/ES/MICINN/MTM2016-76868-C2-2-P info:eu-repo/grantAgreement/ES/MICINN/MTM2013-45710-C2-1-P info:eu-repo/grantAgreement/ES/DGA/E15 info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 1.074 2017 MATHEMATICS 56 / 309 = 0.181 2017 Q1 T1 0.493 2017 Computational Mathematics 2017 Q2 Analysis 2017 Q3 Geometry and Topology 2017 Q3 Algebra and Number Theory 2017 Q3 Applied Mathematics 2017 Q3 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion (orcid)0000-0003-1820-6755 Cogolludo-Agustín, J. I. Universidad de Zaragoza Guerville-Ballé, B. (orcid)0000-0002-6750-8971 Marco-Buzunáriz, M. Universidad de Zaragoza 2006 440 Universidad de Zaragoza Dpto. Matemáticas Área Geometría y Topología 2006 200 Universidad de Zaragoza Dpto. Matemáticas Área Didáctica Matemática 111, 2 (2017), 377-402 Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas 1578-7303 587792 http://zaguan.unizar.es/record/61505/files/texto_completo.pdf Postprint 74925 http://zaguan.unizar.es/record/61505/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:61505 articulos driver 2019-11-13-13:45:17 ARTICLE