Gaps in the support of canonical currents on projective K3 surfaces
Dynamical Systems
2024-01-23 v2 Complex Variables
Abstract
We construct examples of canonical closed positive currents on projective K3 surfaces that are not fully supported on the complex points. The currents are the unique positive representatives in their cohomology classes and have vanishing self-intersection. The only previously known such examples were due to McMullen on non-projective K3 surfaces and were constructed using positive entropy automorphisms with a Siegel disk. Our construction is based on a Zassenhaus-type estimate for commutators of automorphisms.
Keywords
Cite
@article{arxiv.2302.08633,
title = {Gaps in the support of canonical currents on projective K3 surfaces},
author = {Simion Filip and Valentino Tosatti},
journal= {arXiv preprint arXiv:2302.08633},
year = {2024}
}
Comments
14 pages; final version to appear in the Sibony Memorial Volume of the Journal of Geometric Analysis