Lectures on Riemann Surfaces [Otto Forster] on *FREE* shipping on qualifying offers. Lectures on Riemann surfaces, by Otto Forster, Graduate Texts in Math., vol. 81, Springer-Verlag, New York, , viii + pp., $ ISBN What this course is about: Every serious study of analytic functions of one complex variable will need Riemann surfaces. For example, “multi-valued” functions.
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I would also recommend Skrfaces Introduction to Algebraic Curves — a beautiful text based on lectures. Post as a guest Name.
This book grew out of lectures on Riemann surfaces which the author gave at the universities of Munich, Regensburg and Munster.
I found that argument confusing too. Lecture 1, Tuesday, September 16, Definition of Riemann surfaces, first examples. Mumford’s book Complex projective varieties I, also has a terrific chapter on curves from the complex analytic point of view. Surfacess pages Page 2. I do recommend the recent published book by Donaldson on this subject.
reference request – Good book for Riemann Surfaces – Mathematics Stack Exchange
Reference in Riemann Surfaces Ask Question. The Dirichlet Boundary Value Problem. Then we construct the Riemann surfaces which arise via analytic continuation of function germs.
Description This book grew out of lectures on Riemann surfaces given by Otto Forster at the universities of Munich, Regensburg, and Munster. Branched and Unbranched Coverings. Naive Lie Theory John Stillwell. Exercises from Lecture 4 ps-filepdf-file. The argument is similar to zurfaces proof of Nakayama’s lemma. Goodreads is the world’s largest site for readers with over 50 million reviews.
American Mathematical Society, Looking for beautiful books? Can any one recommend me a good introductory book in Riemann Surface? Thanks to Georges Elencwajg for significant corrections to this answer.
Lectures on Riemann Surfaces : Otto Forster :
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Frances Kirwan’s book Complex Algebraic Curves has two really nice chapters on Riemann Surfaces and over all the level of the book is pretty decent to start with. Exercises from Lecture 3 ps-filepdf-file.
Groups and Symmetry Mark A. The more analytic approach is to begin with compact complex one manifolds and prove they are all representable as algebraic curves. Author and Subject Index.
After you learn the basics, the book of Arbarello, Cornalba, Griffiths, Harris, is just amazing. Perspectives on Riemann Surfaces. Of course Riemann’s thesis and followup paper on theory of abelian functions is rather incredible as well.
Miranda’s book is more focused on algebraic curves in general and preparing the reader to go on in algebraic geometry by giving them digestible analytic examples of algebraic constructions they will see in more generality later I think Table of contents 1 Covering Spaces.
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 Combinatorics and Graph Theory John M. Stalks of the structure sheaf. It is clearly written, contains historical comments and a lot of mathematical gems.
Lectures on Riemann Surfaces
And the proof of this is based on the fact that one can locally solve inhomogeneous Cauchy Riemann equations and on Schwarz’ Lemma. Home Questions Tags Users Unanswered. We’re featuring millions of their reader surfxces on our book pages to help you find your new favourite book. Sign up or log in Sign up using Google. Another foster analytic monograph from this point of view is the Princeton lecture notes on Riemann surfaces by Robert Gunning, which is also a good place to learn sheaf theory.
Elements of Algebra John Stillwell. I will check this riemanm. The approach in the wonderful book of Miranda is to consider the functor from algebraic curves to compact complex one manifolds, although he never fully proves it is well defined.
Riemann surfaces, several complex variables, Abelian functions, higher modular functions, Berlin: