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

• 成果类型: Article
• 署名作者: Viet-Anh Nguyen
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lille
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-017-0772-y
• 发表日期: 2018
• 页码: 531-618
• 关键词: riemann surface laminations; harmonic currents; equation

摘要

We study the holonomy cocycle H of a holomorphic foliation F by Riemann surfaces defined on a compact complex projective surface X satisfying the following two conditions: its singularities E are all hyperbolic; there is no holomorphic non-constant map C -> X such that out of E the image of C is locally contained in a leaf. Let T be a harmonic current tangent to F which does not give mass to any invariant analytic curve. Using the leafwise Poincare metric, we show that H is integrable with respect to T. Consequently, we infer the existence of the Lyapunov exponent function of T.