Gaps in the Support of Canonical Currents on Projective K3 Surfaces

Simion Filip, Valentino Tosatti

Research output: Contribution to journalArticlepeer-review


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 nonprojective 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.

Original languageEnglish (US)
Article number76
JournalJournal of Geometric Analysis
Issue number3
StatePublished - Mar 2024


  • Canonical currents
  • Dynamics of automorphisms
  • K3 surfaces

ASJC Scopus subject areas

  • Geometry and Topology


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