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3 results

  • Elliptic Fibrations on K3 Surfaces

  • Viacheslav V. Nikulin
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 57 / Issue 1 / February 2014
    Published online by Cambridge University Press:
    19 December 2013, pp. 253-267
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  • This paper consists mainly of a review and applications of our old results relating to the title. We discuss how many elliptic fibrations and elliptic fibrations with infinite automorphism groups (or Mordell–Weil groups) an algebraic K3 surface over an algebraically closed field can have. As examples of applications of the same ideas, we also consider K3 surfaces with exotic structures: with a finite number of non-singular rational curves, with a finite number of Enriques involutions, and with naturally arithmetic automorphism groups.

  • MODULI CURVES OF SUPERSINGULAR K3 SURFACES IN CHARACTERISTIC 2 WITH ARTIN INVARIANT 2

  • Ichiro Shimada
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 49 / Issue 2 / June 2006
    Published online by Cambridge University Press:
    30 May 2006, pp. 435-503
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  • We construct moduli curves of polarized supersingular K3 surfaces in characteristic 2 with Artin invariant 2. As an application, we detect a ‘jump’ phenomenon in a family of automorphism groups of supersingular K3 surfaces with a constant Néron–Severi lattice.