Vector fields and foliations on compact surfaces of class
Georges Dloussky, Karl Oeljeklaus (1999)
Annales de l'institut Fourier
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It is well-known that minimal compact complex surfaces with containing are in the class VII of Kodaira. In fact, there are no other known examples. In this paper we prove that all surfaces with global spherical shells admit a singular holomorphic foliation. The existence of a numerically anticanonical divisor is a necessary condition for the existence of a global holomorphic vector field. Conversely, given the existence of a numerically anticanonical divisor, surfaces with a global...