Elliptic fibrations on K3 surfaces

TL;DR

This paper reviews various results concerning the number and properties of elliptic fibrations on algebraic K3 surfaces, including those with infinite automorphism groups, summarizing research presented at a 2010 workshop.

Contribution

It consolidates and discusses the author's findings on elliptic fibrations on K3 surfaces, focusing on their quantity and automorphism groups.

Findings

Number of elliptic fibrations on K3 surfaces varies

Existence of elliptic fibrations with infinite automorphism groups

Summary of research presented at Oberwolfach 2010

Abstract

This is mainly a review of my results related to the title. We discuss, how many elliptic fibrations and elliptic fibrations with infinite automorphism group (or the Mordell-Weil group) an algebraic K3 surface over an algebraically closed field can have. This was the subject of my talk at Oberwolfach Workshop "Higher dimensional elliptic fibrations" in October 2010.