1996/07/08 by Frédéric Campana, Jean-Pierre Demailly, Campana, Frédéric +3
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.math/9607215
openalex publication_date 1996/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate compact complex manifolds of dimension three and second Betti number b2(X) = 0. We are interested in the algebraic dimension a(X), which is by definition the transcendence degree of the field of meromorphic functions over the field of complex numbers. The topological Euler characteristic χ top(X) equals the third Chern class c3(X) by a theorem of Hopf. Our main result is that, if X is a compact 3-dimensional complex manifold with b2(X) = 0 and a(X) > 0, then c3(X) = χ\rm top(X) = 0, that is, we either have b1(X) = 0, b3(X) = 2 or b1(X) = 1, b3(X) = 0.