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portada Lectures on Riemann Surfaces
Type
Physical Book
Author
Translated by
Publisher
Language
English
Pages
256
Format
Paperback
Dimensions
23.4x15.6x1.4 cm
Weight
0.38 kg.
ISBN13
9781461259633
Categories

Lectures on Riemann Surfaces

Otto Forster (Author) · Bruce Gilligan (Translated by) · Springer · Paperback

Lectures on Riemann Surfaces - Forster, Otto ; Gilligan, Bruce

New Book Imported to Taiwan
Delivery: 30 Oct - 09 Nov Shipping: 3 to 4 business days.
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NT$ 2,528

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Synopsis "Lectures on Riemann Surfaces"

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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