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Self-intersection of foliation cycles on complex manifolds

Sorbonne Universités, UPMC Univ Paris 06, IMJ-PRG, UMR 7586 CNRS, Univ Paris Diderot, Sorbonne Paris Cité, F-75005, Paris, France

E-mail Address: lucassa@chalmers.se

Present Address: Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, SE-412 96 Goteborg, Sweden

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https://doi.org/10.1142/S0129167X17500549Cited by:4 (Source: Crossref)

Abstract

Let $X$ be a compact Kähler manifold and let $T$ be a foliation cycle directed by a transversely Lipschitz lamination on $X$ . We prove that the self-intersection of the cohomology class of $T$ vanishes as long as $T$ does not contain currents of integration along compact manifolds.

As a consequence, we prove that transversely Lipschitz laminations of low codimension in certain manifolds, e.g. projective spaces, do not carry any foliation cycles except those given by integration along compact leaves.

Keywords:

AMSC: 37F75, 32U40

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