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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The Serre Duality Theorem.
The Universal Covering and Covering Transformations. Riemann surfaces, several complex variables, Abelian functions, higher modular functions, Berlin: Bost, Introduction to compact Riemann surfaces, Jacobians, and abelian varietiesin From number theory to physics Les Houches,Springer, Berlin,pp. The book is divided into three chapters.
A question from Otto Forster’s book on Riemann surfaces – MathOverflow
Dror’s book seems to lead naturally to Demailly’s very heavy book on Complex Analytic and Differential Geometry. Lecture 6, Tuesday, October 21, Divisors. Home Questions Tags Users Unanswered. Another excellent 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. I would also recommend Griffiths’s Introduction to Algebraic Curves — a beautiful text based on lectures.
Complex Analysis Joseph Bak. And the proof of this is based on the fact that one can locally solve inhomogeneous Cauchy Riemann equations and on Schwarz’ Lemma. This book grew out of lectures on Riemann surfaces which the author gave at the universities of Munich, Regensburg and Munster. Exercises from Lecture 6 ps-filepdf-file. A chapter of the Algebraic topology book by Allen Hatcher. Exercises from Lecture 13 ps-filepdf-file.
It is really interesting to read. It also deals quite a bit with non-compact Riemann surfaces, but does include standard material on Abel’s Theorem, the Abel-Jacobi map, etc.
Mumford’s book Complex projective varieties I, also has a terrific chapter on curves from the complex analytic point of view. Ben McKay 14k 2 27 I do recommend the recent published book by Donaldson on this subject.
Of course Riemann’s thesis and followup paper on theory of abelian functions is rather incredible as well.
Lectures on Riemann Surfaces
Holomorphic maps of complex tori. I recommend “Lectures on Riemann Surfaces” by Forster. About Otto Forster Dr. Sign up using Facebook.
Functions with Prescribed Summands of Automorphy. Understanding Analysis Stephen Abbott. In the first chapter we consider Riemann surfaces as covering spaces and develop a few basics from topology which are needed for this. Sign up using Facebook.
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Riemann Surfaces WS /
Thanks to Georges Elencwajg for significant corrections to this answer. Sign up or log in Sign up using Google. Check out the top books of the year on our page Best Books of In particular, it includes pretty much all the analysis to prove finite-dimensionality of sheaf cohomology on riemanh compact Riemann surface.
The more analytic approach is to begin with compact complex one manifolds and prove they are all representable as algebraic curves. Exercises from Lecture 9 ps-filepdf-file. Book ratings by Goodreads. Selected pages Page 2.
Sign up using Facebook. 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.
His main result is that all compact complex one manifolds occur as the Riemann surface of an algebraic curve. How should I understand this theorem? The Definition of Riemann Surfaces.