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Elliptic Fibrations on K3 Surfaces

Published online by Cambridge University Press:  19 December 2013

Viacheslav V. Nikulin
Viacheslav V. Nikulin*
Affiliation:
Department of Pure Mathematics, University of Liverpool, Liverpool L69 3BX, UK (vnikulin@liv.ac.uk) and Steklov Mathematical Institute, ul. Gubkina 8, Moscow 117966, GSP-1, Russia (vvnikulin@list.ru)
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Abstract

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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.

Keywords

K3 surfaceelliptic fibrationPicard latticeautomorphism groupPrimary 14J2814J2714J5014C22
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 1 , February 2014 , pp. 253 - 267
Copyright
Copyright © Edinburgh Mathematical Society 2014 

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