Rocky Mountain Journal of Mathematics

Elliptic Fibrations of Some Extremal $K3$ Surfaces

Matthias Schütt

Full-text: Open access

Article information

Source
Rocky Mountain J. Math., Volume 37, Number 2 (2007), 609-652.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1181068770

Digital Object Identifier
doi:10.1216/rmjm/1181068770

Mathematical Reviews number (MathSciNet)
MR2333389

Zentralblatt MATH identifier
1133.14037

Subjects
Primary: 14J27: Elliptic surfaces 14J28: $K3$ surfaces and Enriques surfaces

Citation

Schütt, Matthias. Elliptic Fibrations of Some Extremal $K3$ Surfaces. Rocky Mountain J. Math. 37 (2007), no. 2, 609--652. doi:10.1216/rmjm/1181068770. https://projecteuclid.org/euclid.rmjm/1181068770


Export citation

References

  • E. Artal Bartolo, H. Tokunaga and D.Q. Zhang, Miranda-Persson's problem on extremal elliptic $K3$ surfaces, Pacific J. Math. 202 (2002), 37-72.
  • A. Beauville, Les familles stables de courbes elliptiques sur $\P^1$ admettant quatre fibres singulie, C.R. Acad. Sci. Paris 294 (1982), 657-660.
  • S. Herfurtner, Elliptic surfaces with four singular fibres, Math. Ann. 291 (1991), 319-342.
  • Y. Iron, An explicit representation of a $K3$ elliptic surface that realizes [1,1,1,1,1,19], M.Sc. Thesis, Hebrew University of Jerusalem, 2003.
  • K. Kodaira, On compact analytic surfaces I-III, Ann. of Math. 71 (1960), 111-152; 77 (1963), 563-626; 78 (1963), 1-40.
  • R. Livné and N. Yui, The modularity of certain non-rigid Calabi-Yau threefolds, J. Math. Kyoto Univ. 45 (2005), 645-665.
  • R. Miranda, The basic theory of elliptic surfaces, Dottorato di ricerca in matematica, ETS Editrice, Pisa, 1989.
  • R. Miranda, Persson's list of singular fibers for a rational elliptic surface, Math. Z. 205 (1990), 191-211.
  • R. Miranda and U. Persson, On extremal rational elliptic surfaces, Math. Z. 193 (1986), 537-558.
  • --------, Configurations of $I_n$ fibers on elliptic $K 3$ surfaces, Math. Z. 201 (1989), 339-361.
  • --------, Mordell-Weil groups of extremal elliptic $K3$ surfaces, in Problems in the theory of surfaces and their classification (Cortona 1988), Sympos. Math., vol. 32, Academic Press, London, 1991, 167-192.
  • K.-V. Nguyen, Extremal elliptic fibrations and singular $K3$ surfaces, Tokyo J. Math. 22 (1999), 415-424.
  • U. Persson, Double sextics and singular $K3$ surfaces, in Algebraic geometry (Sitges 1983), Lecture Notes in Math., vol. 1124, Springer, New York, 1985, pp. 262-328.
  • U. Schmickler-Hirzebruch, Elliptische Flächen über $\bf P_1\C$ mit drei Ausnahmefasern und die hypergepmetrische Differentialgleichung, Schriftenreihe Math. Inst. Univ. Münster, 1985.
  • I. Shimada and D.-Q. Zhang, Classification of extremal elliptic $K3$ surfaces and fundamental groups of open $K3$ surfaces, Nagoya Math. J. 161 (2001), 23-54.
  • T. Shioda, The elliptic $K3$ surfaces with a maximal singular fibre, C.R. Acad. Sci. Paris 337 (2003), 461-466.
  • T. Shioda and H. Inose, On singular $K3$ surfaces, in Complex analysis and algebraic geometry (W.L. Baily, Jr. and T. Shioda, eds.), Iwanami Shoten, Tokyo, 1977, pp. 119-136.
  • J. Silverman, Advanced topics in the arithmetic of elliptic curves, Springer-Verlag, Berlin, 1994.
  • J. Top and N. Yui, Explicit equations of some elliptic modular surfaces, Rocky Mountain J. Math. 37 (2007), pp. 663-687.