SURFACES DE LA CLASSE VII_0 ADMETTANT UN CHAMP DE VECTEURS

Matei TOMA

The paper is published: Comment. Math. Helv., 75 (2000), 255-270

MSC 2000

32J15 Compact surfaces

Abstract
We prove that a surface of class $VII_0$ with $b_2≥0$ and admitting a non-trivial holomorphic vector field contains exactly $b_2$ rational curves. By a theorem of I.Nakamura it follows that such a surface is a deformation of a blown-up primary Hopf surface. This result contributes to the classification of compact complex surfaces with vector fields.