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arXiv:1403.7688 [math.DS]AbstractReferencesReviewsResources

Singular holomorphic foliations by curves I: Integrability of holonomy cocycle in dimension 2

Viet-Anh Nguyen

Published 2014-03-30, updated 2016-04-19Version 2

We study the holonomy cocycle H of a holomorphic foliation \Fc by Riemann surfaces defined on a compact complex projective surface X satisfying the following two conditions: 1) its singularities E are all hyperbolic; 2) there is no holomorphic non-constant map \C\to X such that out of E the image of \C is locally contained in leaves. Let T be a harmonic current tangent to \Fc which does not give mass to any invariant analytic curve. Using the leafwise Poincar\'e metric, we show that H is integrable with respect to T.

Comments: 64 pages. In this second version we have revised the article entirely
Categories: math.DS, math.CV, math.DG
Subjects: 37A30, 57R30, 58J35, 58J65, 60J65
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