Titlebook: Riemann Surfaces and Generalized Theta Functions; Robert C. Gunning Book 1976 Springer-Verlag Berlin Heidelberg 1976 Division.Equivalence.

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Book 1976nected Riemann surface M of genus g is realized by an irreducible (g -1)-dimensional analytic subvariety, an irreducible hypersurface, of the associated g-dimensional complex torus J(M); this hyper- 1 surface W- r;;;, J(M) is the image of the natural mapping Mg- -+J(M), and is g 1 1 birationally equ

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978-3-642-66384-0Springer-Verlag Berlin Heidelberg 1976

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Complex Manifolds and Vector Bundles,et of the .-dimensional number space ?.. A . {., .} of such a manifold . consists of a covering of . by open subsets . together with homeomorphisms .:.→. between the sets . and open subsets .??.; the sets . are called . and the mappings . are called .. A topological manifold of course always admits

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Riemann Surfaces,me familiarity with the topology of surfaces will be presupposed; so it can be taken as known that topologically . is a sphere with . handles, where the integer . is called the genus of the surface. The surface M can then be dissected into a contractible set by cutting along 2. paths which issue fro

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Book 1976long been basic to the study both of Riemann surfaces and of complex tori. A Riemann surface is naturally imbedded as an analytic submanifold in its associated torus; and various spaces of linear equivalence elasses of divisors on the surface (or equivalently spaces of analytic equivalence elasses o