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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Effective invariants of braid monodromy


Authors: Enrique Artal Bartolo, Jorge Carmona Ruber and José Ignacio Cogolludo Agustín
Journal: Trans. Amer. Math. Soc. 359 (2007), 165-183
MSC (2000): Primary 14D05, 14H30, 14H50, 68W30
Published electronically: August 16, 2006
MathSciNet review: 2247887
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Abstract: In this paper we construct new invariants of algebraic curves based on (not necessarily generic) braid monodromies. Such invariants are effective in the sense that their computation allows for the study of Zariski pairs of plane curves. Moreover, the Zariski pairs found in this work correspond to curves having conjugate equations in a number field, and hence are not distinguishable by means of computing algebraic coverings. We prove that the embeddings of the curves in the plane are not homeomorphic. We also apply these results to the classification problem of elliptic surfaces.


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Additional Information

Enrique Artal Bartolo
Affiliation: Departamento de Matemáticas, Campus Plaza de San Francisco s/n, E-50009 Zara- goza, Spain
Email: artal@unizar.es

Jorge Carmona Ruber
Affiliation: Departamento de Sistemas Informáticos y Programación, Universidad Complutense, Ciudad Universitaria s/n, E-28040 Madrid, Spain
Email: jcarmona@sip.ucm.es

José Ignacio Cogolludo Agustín
Affiliation: Departamento de Matemáticas, Campus Plaza de San Francisco s/n, E-50009 Zara- goza, Spain
Email: jicogo@unizar.es

DOI: http://dx.doi.org/10.1090/S0002-9947-06-03881-5
PII: S 0002-9947(06)03881-5
Keywords: Braid monodromy, plane curve, group representations
Received by editor(s): January 26, 2004
Received by editor(s) in revised form: October 13, 2004
Published electronically: August 16, 2006
Additional Notes: The first and third authors were partially supported by MTM2004-08080-C02-02. The second author was partially supported by MTM2004-08080-C02-01
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.