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.

arXiv comment70 pages, 3 figures; final version to appear in the Cambridge Journal of Mathematics

References in corpus (4)

• Collapsing hyperkähler manifolds
• Automorphisms of surfaces: Kummer rigidity and measure of maximal entropy
• Kummer rigidity for K3 surface automorphisms via Ricci-flat metrics
• 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