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On Dihedral Galois Coverings

Published online by Cambridge University Press:  20 November 2018

Hiro-o Tokunaga
Hiro-o Tokunaga*
Affiliation:
Department of Mathematics, Kochi University, Kochi 780, Japan, e-mail: [email protected]
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Abstract

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In this paper, we shall give a method in constructing dihedral Galois covering with prescribed branch locus. As an application, we shall look into dihedral Galois covering of P2, where torsion elements of the Mordell-Weil group of an elliptic surface play key roles in constructing coverings

Keywords

14E2014E3514J27
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 6 , 01 December 1994 , pp. 1299 - 1317
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Cox, D., Mordell-Weil groups of elliptic curves over C(t) with pg = 0 or 1, Duke Math. J. 49(1982), 677–689.Google Scholar
2. Cox, D. and Parry, W., Torsion in elliptic curves overk(t), Compositio Math. 41(1980), 337–354.Google Scholar
3. Deligne, P., Le groupe fondamental du complément d'une courbe plane n'ayant que des point double ordinaires estabélien, Sém. Bourbaki 543, Springer Lecture Notes in Math. 842, 1981, 1–10.Google Scholar
4. Fulton, W., On the fundamental group of the complement of a node curve, Ann. of Math. 111(1980), 407–409.Google Scholar
5. Fulton, W., Intersection Theory, Ergeb. Math. Grenzgeb. (3), Folge 2, Springer-Verlag, 1984.Google Scholar
6. Horikawa, E., On deformation of quintic surfaces, Invent. Math. 31(1975), 43–85.Google Scholar
7. Iitaka, S., Algebraic Geometry, Graduate Texts in Math. 76, Springer-Verlag, 1982.Google Scholar
8. Kodaira, K., On compact analytic surfaces II, Ann. of Math. 77(1963), 563–626.Google Scholar
9. Miranda, R. and Persson, U., On extremal rational elliptic surfaces, Math. Z. 193(1986), 537–558.Google Scholar
10. Miranda, R., Torsion groups of elliptic surfaces, Compositio Math. 72(1989), 249–267.Google Scholar
11. Namba, M., Branched coverings and algebraic functions, Pitman Research Notes in Math. 161, 1987.Google Scholar
12. Pardini, R., Abelian covers of algebraic varieties, J. Reine Angew. Math. 417(1991), 191–213.Google Scholar
13. Persson, U., Configuration of Kodaira fiber on rational elliptic surfaces, Math. Z. 205(1990), 1–47.Google Scholar
14. Shioda, T., On the Mordell-Weil lattices, Comment. Math. Univ. St. Paul. 39(1990), 211–240.Google Scholar
15. Zariski, O., On the problem of existence of algebraic functions of two variables possessing a given branch curve, Amer. J. Math. 51(1929), 305–328.Google Scholar