Reconstruction of general elliptic K3 surfaces from their Gromov-Hausdorff limits

Abstract

We show that a general elliptic K3 surface with a section is determined uniquely by its discriminant, which is a configuration of 24 points on the projective line. It follows that a general elliptic K3 surface with a section can be reconstructed from its Gromov-Hausdorff limit as the volume of the fiber goes to zero.

7 pages; v2: Revised reflecting comments of the referees and remarks by Remke Kloosterman