2021/10/10 by Takayuki Koike, Koike, Takayuki · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Meromorphic and Entire Functions #Primary 32M25 #Secondary 14C20
paper · pdf · doi:10.48550/arxiv.2110.04864
openalex publication_date 2021/10/10 · openalex created_date 2021/10/25 · openalex updated_date 2026/07/28
Let X be a compact Kähler manifold and α be a class in the Dolbeault cohomology class of bidegree (1, 1) on X. When the numerical dimension of α is one and α admits at least two smooth semi-positive representatives, we show the existence of a family of real analytic Levi-flat hypersurfaces in X and a holomorphic foliation on a suitable domain of X along whose leaves any semi-positive representative of α is zero. As an application, we give the affirmative answer to \cite[Conjecture 2.1]K2019 on the relation between the semi-positivity of the line bundle [Y] and the analytic structure of a neighborhood of Y for a smooth connected hypersurface Y of X.