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Pencils and infinite dihedral covers of 
Authors:
Enrique Artal Bartolo, José Ignacio Cogolludo and Hiro-o Tokunaga
Journal:
Proc. Amer. Math. Soc. 136 (2008), 21-29
MSC (2000):
Primary 14H30, 14B05
Posted:
October 18, 2007
MathSciNet review:
2350384
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Additional Information
Abstract: In this work we study the connection between the existence of finite dihedral covers of the projective plane ramified along an algebraic curve  , infinite dihedral covers, and pencils of curves containing  .
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E.
Artal, J.
Carmona, J.
I. Cogolludo, and Hiro-O
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Knot Theory Ramifications 10 (2001), no. 4,
547–578. MR 1831676
(2002c:14047), http://dx.doi.org/10.1142/S0218216501001001
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E. Artal, J.I. Cogolludo-Agustín and H. Tokunaga: Nodal degenerations of plane curves and Galois covers, preprint, 2004.
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(34 #6789)
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Ignacio Cogolludo, Fundamental group for some cuspidal curves,
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(2000h:14021), http://dx.doi.org/10.1112/S0024609398005323
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(2000m:14015), http://dx.doi.org/10.1090/S0002-9947-00-02524-1
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(2005g:14033), http://dx.doi.org/10.2206/kyushujm.57.411
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- E. Artal, J. Carmona, J.I. Cogolludo, and H. Tokunaga, Sextics with singular points in special position, J. Knot Theory Ramifications 10 (2001), no. 4, 547-578. MR 1831676 (2002c:14047)
- 2.
- E. Artal, J.I. Cogolludo-Agustín and H. Tokunaga: Nodal degenerations of plane curves and Galois covers, preprint, 2004.
- 3.
- E. Brieskorn: Über die Auflösung gewisser Singularitäten von holomorpher Abbildungen, Math. Ann. 166 (1966), 76-102. MR 0206973 (34:6789)
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- -: Über die Auflösung der rationalen Singularitäten holomorpher Abbildungen, Math. Ann. 178 (1968), 255-270. MR 0206973 (34:6789)
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- J.I. Cogolludo-Agustín: Fundamental group for some cuspidal curves, Bull. London Math. Soc. 31 (1999), no. 2, 136-142. MR 1664168 (2000h:14021)
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- E. Horikawa: On deformation of quintic surfaces, Invent. Math. 31 (1975), 43-85.
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- H. Tokunaga: On dihedral Galois covers, Canadian J. of Math. 46 (1994), 1299-1317. MR 1304347 (96d:14015)
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- -: Dihedral coverings of algebraic surfaces and their application, Trans. Amer. Math.Soc. 352 (2000), 4007-4017. MR 1675238 (2000m:14015)
- 9.
- H. Tsuchihashi: Galois coverings of projective varieties for dihedral group and symmetric groups, Kyushu J. Math. 57 (2003), 411-427. MR 2050094 (2005g:14033)
- 10.
- O. Zariski: On the problem of existence of algebraic functions of two variables possessing a given branch curve, Amer. J. Math. 51 (1929), 305-328. MR 1506719
- 11.
- -: On the purity of the branch locus of algebraic functions, Proc. Nat. Acad. USA 44 (1958), 791-796. MR 0095846 (20:2344)
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Additional Information
Enrique Artal Bartolo
Affiliation:
Departamento de Matemáticas, Universidad de Zaragoza, Campus Plaza San Francisco s/n, E-50009 Zaragoza, Spain
Email:
artal@unizar.es
José Ignacio Cogolludo
Affiliation:
Departamento de Matemáticas, Universidad de Zaragoza, Campus Plaza San Francisco s/n, E-50009 Zaragoza, Spain
Email:
jicogo@unizar.es
Hiro-o Tokunaga
Affiliation:
Department of Mathematics, Tokyo Metropolitan University, Minamiohsawa Hachoji, 192-0357 Tokyo, Japan
Email:
tokunaga@comp.metro-u.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002-9939-07-08965-4
PII:
S 0002-9939(07)08965-4
Keywords:
Galois cover,
degeneration of curves
Received by editor(s):
October 20, 2005
Received by editor(s) in revised form:
August 23, 2006
Posted:
October 18, 2007
Additional Notes:
The research of the first and second authors was partially supported by BFM2001-1488-C02-02
Communicated by:
Michael Stillman
Article copyright:
© Copyright 2007 American Mathematical Society
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