Holomorphic plane fields with many invariant hypersurfaces

2015/03/26 by Leonardo Câmara, L. Câmara, Câmara, L. +3
Mathematics · #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #math.DS

paper · pdf · doi:10.48550/arxiv.1503.07618

arxiv created 2015/03/26 · openalex publication_date 2015/03/26 · arxiv updated 2015/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we show that a (non necessarily integrable) holomorphic plane field on a compact complex manfold M having an infinite number of invariant hypersurfaces must admit a meromorphic first integral F:M\longrightarrow ℂ^p. In particular, it is integrable.

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