FORSTER RIEMANN SURFACES PDF

I found that argument confusing too. Riemann surfaces In particular this includes the Riemann surfaces of algebraic functions. In particular, it includes pretty much all the analysis to prove finite-dimensionality of sheaf cohomology on a compact Riemann surface. Understanding Analysis Stephen Abbott.

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About this book Introduction This book grew out of lectures on Riemann surfaces which the author gave at the universities of Munich, Regensburg and Munster. Its aim is to give an introduction to this rich and beautiful subject, while presenting methods from the theory of complex manifolds which, in the special case of one complex variable, turn out to be particularly elementary and transparent.

The book is divided into three chapters. In the first chapter we consider Riemann surfaces as covering spaces and develop a few basics from topology which are needed for this. Then we construct the Riemann surfaces which arise via analytic continuation of function germs. In particular this includes the Riemann surfaces of algebraic functions. As well we look more closely at analytic functions which display a special multi-valued behavior. Examples of this are the primitives of holomorphic i-forms and the solutions of linear differential equations.

The second chapter is devoted to compact Riemann surfaces. Sheaf cohomology is an important technical tool. But only the first cohomology groups are used and these are comparatively easy to handle.

The main theorems are all derived, following Serre, from the finite dimensionality of the first cohomology group with coefficients in the sheaf of holomorphic functions.

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Lectures on Riemann Surfaces

The final prices may differ from the prices shown due to specifics of VAT rules About this Textbook This book grew out of lectures on Riemann surfaces which the author gave at the universities of Munich, Regensburg and Munster. Its aim is to give an introduction to this rich and beautiful subject, while presenting methods from the theory of complex manifolds which, in the special case of one complex variable, turn out to be particularly elementary and transparent. The book is divided into three chapters. In the first chapter we consider Riemann surfaces as covering spaces and develop a few basics from topology which are needed for this. Then we construct the Riemann surfaces which arise via analytic continuation of function germs. In particular this includes the Riemann surfaces of algebraic functions. As well we look more closely at analytic functions which display a special multi-valued behavior.

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