Surfaces of class VII0 with vector fields

Abstract

We show that a minimal surface of class VII0 with b(2) > 0 which admits a nontrivial holomorphic vector field contains exactly bz rational curves. By a theorem of I. Nakamura this implies that such a surface is a deformation of a blown-up primary Hopf surface. This result clarifies the classification of compact complex surfaces with holomorphic vector fields. (C) 1999 Academie des Sciences/Editions scientifiques et medicales Elsevier SAS.