Kitagawa, Shinya
Maximal Mordell-Weil lattices of fibred surfaces with p g =q=0
Rendiconti del Seminario Matematico della Università di Padova, Tome 117 (2007) , p. 205-230
Zbl 1139.14031 | MR 2351796
URL stable : http://www.numdam.org/item?id=RSMUP_2007__117__205_0

Bibliographie

[1] E. Arbarello - M. Cornalba - P. A. Griffiths J. Harris, Geometry of Algebraic Curves, Volume I, GMW 267, Springer-Verlag, 1985. MR 770932 | Zbl 0559.14017

[2] M. Coppens - G. Martens, Secant spaces and Clifford's theorem, Compositio Math., 78 (1991), pp. 193-212. Numdam | MR 1104787 | Zbl 0741.14035

[3] M. Demazure - H. Pinkham - B. Teissier, Séminaire sur les Singularités des Surfaces, Lec. Notes in Math., 777 (Springer, Berlin, 1980), pp. viii+339. MR 579026 | Zbl 0415.00010

[4] P. Deligne - N. Katz (eds), Groupes de monodromie en géométrie algébrique II. Séminaire de Géométrie Algébrique de Bois-Marie, 1967-1969 (SGA 7 II), Lec. Notes in Math., 340 (Springer-Verlag, Berlin New York, 1973) pp. x+438. MR 354657 | Zbl 0258.00005

[5] R. Hartshorne, Curves with high self-intersection on algebraic surfaces. Publ. Math. IHES 36 (1969), pp. 111-125. Numdam | MR 266924 | Zbl 0197.17505

[6] S. Iitaka, On irreducible plane curves, Saitama Math. J., 1 (1983), pp. 47-63. MR 717927 | Zbl 0517.14009

[7] S. Kitagawa, On Mordell-Weil lattices of bielliptic fibrations on rational surfaces, J. Math. Soc. Japan, 57 (2005), pp. 137-155. MR 2114725 | Zbl 1093.14051

[8] S. Kitagawa - K. Konno, Fibred rational surfaces with extremal MordellWeil lattices, Math. Z., 251 (2005), pp. 179-204. MR 2176471 | Zbl 1082.14038

[9] G. Martens, The gonality of curves on a Hirzebruch surface, Arch. Math., 67 (1996), pp. 349-352. MR 1407339 | Zbl 0872.14022

[10] A. Noma, Very ample line bundles on regular surfaces obtained by projection, preprint (received September 2nd, 2005). MR 2271360 | Zbl 1108.14008

[11] M.-H. Saito - V. Nguyen Khac, On Mordell-Weil lattices for nonhyperelliptic fibrations of surfaces with zero geometric genus and irregularity, Izv. Ross. Akad. Nauk Ser. Mat., 66 (2002), pp. 137-154. MR 1942097 | Zbl 1053.14043

[12] M.-H. Saito - K. Sakakibara, On Mordell-Weil lattices of higher genus fibrations on rational surfaces, J. Math. Kyoto Univ., 34 (1994), pp. 859-871. MR 1311624 | Zbl 0860.14034

[13] T. Shioda, Mordell-Weil lattices for higher genus fibration over a curve. New trends in algebraic geometry (Warwick, 1996), pp. 359-373, London Math. Soc. Lecture Note Ser., 264, Cambridge Univ. Press, Cambridge, 1999. MR 1714831 | Zbl 0947.14012