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 ...
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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. The main classical results, like the Riemann-Roch Theorem, Abel's Theorem and the Jacobi inversion problem, are presented. 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. And the proof of this is based on the fact that one can locally solve inhomogeneous Cauchy Riemann equations and on Schwarz' Lemma.
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Add this copy of Lectures on Riemann Surfaces to cart. $57.96, good condition, Sold by HPB-Red rated 5.0 out of 5 stars, ships from Dallas, TX, UNITED STATES, published 1981 by Springer.
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Add this copy of Lectures on Riemann Surfaces (Graduate Texts in to cart. $64.42, fair condition, Sold by Anybook rated 4.0 out of 5 stars, ships from Lincoln, UNITED KINGDOM, published 1981 by Springer-Verlag.
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This is an ex-library book and may have the usual library/used-book markings inside. This book has hardback covers. Book contains pencil markings. In fair condition, suitable as a study copy. No dust jacket. Please note the Image in this listing is a stock photo and may not match the covers of the actual item, 650grams, ISBN: 0387906177.
Add this copy of Lectures on Riemann Surfaces to cart. $65.71, like new condition, Sold by GreatBookPrices rated 4.0 out of 5 stars, ships from Columbia, MD, UNITED STATES, published 1981 by Springer.
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Fine. Sewn binding. Cloth over boards. 256 p. Contains: Unspecified. Graduate Texts in Mathematics, 81. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
Add this copy of Lectures on Riemann Surfaces to cart. $78.41, new condition, Sold by GreatBookPrices rated 4.0 out of 5 stars, ships from Columbia, MD, UNITED STATES, published 1981 by Springer.
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New. Sewn binding. Cloth over boards. 256 p. Contains: Unspecified. Graduate Texts in Mathematics, 81. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
Add this copy of Lectures on Riemann Surfaces to cart. $78.42, new condition, Sold by Ria Christie Books rated 5.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 1981 by Springer.