Maximal Mordell-Weil lattices of fibred surfaces with p g = q = 0

Shinya Kitagawa

Rendiconti del Seminario Matematico della Università di Padova (2007)

  • Volume: 117, page 205-230
  • ISSN: 0041-8994

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Kitagawa, Shinya. "Maximal Mordell-Weil lattices of fibred surfaces with $p_g=q=0$." Rendiconti del Seminario Matematico della Università di Padova 117 (2007): 205-230. <http://eudml.org/doc/108713>.

@article{Kitagawa2007,
author = {Kitagawa, Shinya},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
language = {eng},
pages = {205-230},
publisher = {Seminario Matematico of the University of Padua},
title = {Maximal Mordell-Weil lattices of fibred surfaces with $p_g=q=0$},
url = {http://eudml.org/doc/108713},
volume = {117},
year = {2007},
}

TY - JOUR
AU - Kitagawa, Shinya
TI - Maximal Mordell-Weil lattices of fibred surfaces with $p_g=q=0$
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2007
PB - Seminario Matematico of the University of Padua
VL - 117
SP - 205
EP - 230
LA - eng
UR - http://eudml.org/doc/108713
ER -

References

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  3. [3] M. DEMAZURE - H. PINKHAM - B. TEISSIER, Séminaire sur les Singularités des Surfaces, Lec. Notes in Math., 777 (Springer, Berlin, 1980), pp. viii+339. Zbl0415.00010MR579026
  4. [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. Zbl0258.00005MR354657
  5. [5] R. HARTSHORNE, Curves with high self-intersection on algebraic surfaces. Publ. Math. IHES 36 (1969), pp. 111-125. Zbl0197.17505MR266924
  6. [6] S. IITAKA, On irreducible plane curves, Saitama Math. J., 1 (1983), pp. 47-63. Zbl0517.14009MR717927
  7. [7] S. KITAGAWA, On Mordell-Weil lattices of bielliptic fibrations on rational surfaces, J. Math. Soc. Japan, 57 (2005), pp. 137-155. Zbl1093.14051MR2114725
  8. [8] S. KITAGAWA - K. KONNO, Fibred rational surfaces with extremal MordellWeil lattices, Math. Z., 251 (2005), pp. 179-204. Zbl1082.14038MR2176471
  9. [9] G. MARTENS, The gonality of curves on a Hirzebruch surface, Arch. Math., 67 (1996), pp. 349-352. Zbl0872.14022MR1407339
  10. [10] A. NOMA, Very ample line bundles on regular surfaces obtained by projection, preprint (received September 2nd, 2005). Zbl1108.14008MR2271360
  11. [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. Zbl1053.14043MR1942097
  12. [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. Zbl0860.14034MR1311624
  13. [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. Zbl0947.14012MR1714831

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