Abstract
LetX be a holomorphically convex complex surface that admits an action of the group ℂ* and letp : X → Y be the holomorphic hull. In this article we consider the case thatY is a complex curve and present an equivariant classification of the surfacesX in this situation. Together with existing classifications of Stein resp. compact ℂ*-surfaces, these results provide a complete description of the geometry of holomorphically convex ℂ*-surfaces.
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