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Effective invariants of braid monodromy
Author(s):
Enrique
Artal Bartolo;
Jorge
Carmona Ruber;
José
Ignacio
Cogolludo Agustín
Journal:
Trans. Amer. Math. Soc.
359
(2007),
165-183.
MSC (2000):
Primary 14D05, 14H30, 14H50, 68W30
Posted:
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 Zaragoza,
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 Zaragoza,
Spain
Email:
jicogo@unizar.es
DOI:
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
Posted:
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
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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