Gaps in the Support of Canonical Currents on Projective K3 Surfaces

Simion Filip; Valentino Tosatti

doi:10.1007/s12220-023-01526-0

Gaps in the Support of Canonical Currents on Projective K3 Surfaces

Simion Filip, Valentino Tosatti

Mathematics

Research output: Contribution to journal › Article › peer-review

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 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 language	English (US)
Article number	76
Journal	Journal of Geometric Analysis
Volume	34
Issue number	3
DOIs	https://doi.org/10.1007/s12220-023-01526-0
State	Published - Mar 2024

Keywords

Canonical currents
Dynamics of automorphisms
K3 surfaces

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s12220-023-01526-0

Cite this

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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 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.",

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AB - 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.

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Gaps in the Support of Canonical Currents on Projective K3 Surfaces

Abstract

Keywords

ASJC Scopus subject areas

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