On Dihedral Galois Coverings
Canadian journal of mathematics, Tome 46 (1994) no. 6, pp. 1299-1317

Voir la notice de l'article provenant de la source Cambridge University Press

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
DOI : 10.4153/CJM-1994-074-4
Mots-clés : 14E20, 14E35, 14J27
Tokunaga, Hiro-o. On Dihedral Galois Coverings. Canadian journal of mathematics, Tome 46 (1994) no. 6, pp. 1299-1317. doi: 10.4153/CJM-1994-074-4
@article{10_4153_CJM_1994_074_4,
     author = {Tokunaga, Hiro-o},
     title = {On {Dihedral} {Galois} {Coverings}},
     journal = {Canadian journal of mathematics},
     pages = {1299--1317},
     year = {1994},
     volume = {46},
     number = {6},
     doi = {10.4153/CJM-1994-074-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1994-074-4/}
}
TY  - JOUR
AU  - Tokunaga, Hiro-o
TI  - On Dihedral Galois Coverings
JO  - Canadian journal of mathematics
PY  - 1994
SP  - 1299
EP  - 1317
VL  - 46
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1994-074-4/
DO  - 10.4153/CJM-1994-074-4
ID  - 10_4153_CJM_1994_074_4
ER  - 
%0 Journal Article
%A Tokunaga, Hiro-o
%T On Dihedral Galois Coverings
%J Canadian journal of mathematics
%D 1994
%P 1299-1317
%V 46
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1994-074-4/
%R 10.4153/CJM-1994-074-4
%F 10_4153_CJM_1994_074_4

[1] 1. Cox, D., Mordell-Weil groups of elliptic curves over C(t) with p = 0 or 1, Duke Math. J. 49(1982), 677–689. Google Scholar

[2] 2. Cox, D. and Parry, W., Torsion in elliptic curves overk(t), Compositio Math. 41(1980), 337–354. Google Scholar

[3] 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] 4. Fulton, W., On the fundamental group of the complement of a node curve, Ann. of Math. 111(1980), 407–409. Google Scholar

[5] 5. Fulton, W., Intersection Theory, Ergeb. Math. Grenzgeb. (3), Folge 2, Springer-Verlag, 1984. Google Scholar

[6] 6. Horikawa, E., On deformation of quintic surfaces, Invent. Math. 31(1975), 43–85. Google Scholar

[7] 7. Iitaka, S., Algebraic Geometry, Graduate Texts in Math. 76, Springer-Verlag, 1982. Google Scholar

[8] 8. Kodaira, K., On compact analytic surfaces II, Ann. of Math. 77(1963), 563–626. Google Scholar

[9] 9. Miranda, R. and Persson, U., On extremal rational elliptic surfaces, Math. Z. 193(1986), 537–558. Google Scholar

[10] 10. Miranda, R., Torsion groups of elliptic surfaces, Compositio Math. 72(1989), 249–267. Google Scholar

[11] 11. Namba, M., Branched coverings and algebraic functions, Pitman Research Notes in Math. 161, 1987. Google Scholar

[12] 12. Pardini, R., Abelian covers of algebraic varieties, J. Reine Angew. Math. 417(1991), 191–213. Google Scholar

[13] 13. Persson, U., Configuration of Kodaira fiber on rational elliptic surfaces, Math. Z. 205(1990), 1–47. Google Scholar

[14] 14. Shioda, T., On the Mordell-Weil lattices, Comment. Math. Univ. St. Paul. 39(1990), 211–240. Google Scholar

[15] 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

Cité par Sources :