Degeneracy of holomorphic maps via orbifolds

Erwan Rousseau

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It is well-known that minimal compact complex surfaces with $b_{2} > 0$ containing are in the class VII $_{0}$ 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...

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