Gaps in the support of canonical currents on projective K3 surfaces

Simion Filip; Valentino Tosatti

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Gaps in the support of canonical currents on projective K3 surfaces

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arxiv 2302.08633 v2 pith:LCDHDKK6 submitted 2023-02-17 math.DS math.CV

Gaps in the support of canonical currents on projective K3 surfaces

Simion Filip , Valentino Tosatti This is my paper

classification math.DS math.CV

keywords currentspositivesurfacesautomorphismscanonicalexamplesprojectivewere

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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.

Gaps in the support of canonical currents on projective K3 surfaces

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