Canonical currents and heights for K3 surfaces

Abstract

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.

70 pages, 3 figures; final version to appear in the Cambridge Journal of Mathematics

References in corpus (2)

• Automorphisms of surfaces: Kummer rigidity and measure of maximal entropy
• Elliptic surfaces and intersections of adelic $\mathbb{R}$-divisors

Cited by in corpus (4)

• Gaps in the support of canonical currents on projective K3 surfaces
• Ricci-flat metrics on Calabi-Yau manifolds
• The volume of a divisor and cusp excursions of geodesics in hyperbolic manifolds
• Semipositive line bundles and (1,1)-classes