Configurations of Kodaira fibers on rational elliptic surfaces. (English) Zbl 0722.14021
All possible configurations (about 400) of Kodaira fibers on elliptic rational surfaces are listed, together with their realisations (as Weierstrass models), the rank and torsion of their Mordell-Weil groups of sections. - The classification is first reduced to that of plane quartics with only simple singularities and one special point.
[See also R. Miranda, ibid. 205, No.2, 191-211 (1990; see the following review).]
[See also R. Miranda, ibid. 205, No.2, 191-211 (1990; see the following review).]
Reviewer: F.Campana (Vandoeuvre-les-Nancy)
MSC:
| 14J26 | Rational and ruled surfaces |
| 14J27 | Elliptic surfaces, elliptic or Calabi-Yau fibrations |
| 14J10 | Families, moduli, classification: algebraic theory |
| 14N10 | Enumerative problems (combinatorial problems) in algebraic geometry |
Keywords:
configurations of Kodaira fibers on elliptic rational surfaces; Weierstrass models; Mordell-Weil groupsCitations:
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