Cambridge Journal of Mathematics

Volume 11 (2023)

Number 3

Canonical currents and heights for K3 surfaces

Pages: 699 – 794



Simion Filip (Department of Mathematics, University of Chicago, Illinois, U.S.A.)

Valentino Tosatti (Courant Institute of Mathematical Sciences, New York University, New York, N.Y., U.S.A.)


We construct canonical positive currents and heights on the boundary of the ample cone of a K3 surface. These are equivariant for the automorphism group and fit together into a continuous family, defined over an enlarged boundary of the ample cone. Along the way, we construct preferred representatives for certain height functions and currents on elliptically fibered surfaces.

2010 Mathematics Subject Classification

Primary 37Fxx. Secondary 14J28, 14J50, 32Q20, 32U40, 37P30.

Received 29 November 2021

Published 8 August 2023