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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Thanks to Georges Elencwajg surfades significant corrections to this answer. The Triviality of Vector Bundles. 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 Euclid and Beyond Robin Hartshorne.
Lectures on Riemann Surfaces
It also deals quite a bit with non-compact Riemann surfaces, but surffaces include standard material on Abel’s Theorem, the Abel-Jacobi map, etc. The second chapter is devoted to compact Riemann surfaces.
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A question from Otto Forster’s book on Riemann surfaces – MathOverflow
Since you are both familiar with Forster’s book and with Riemann surfaces, is there any other nice books you can recommend me to take as a reference? Groups and Symmetry Mark A. 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.
Exercises from Lecture 10 ps-filepdf-file. Actually, I am taking part in a reading course where Forster’s book is assigned as the textbook. Branched and Unbranched Coverings. Another excellent analytic monograph from this surfacds of view is the Princeton lecture notes on Riemann surgaces by Robert Gunning, which is also a good place to learn sheaf theory. Abel-Jacobi theorem and its first corollaries.
I found the book very clearly written, very pedagogical and an excellent reference. Selected pages Page 2. Griffiths, Philip; Harris, Joseph.
Dror’s book seems to lead naturally to Demailly’s very heavy book on Complex Analytic and Differential Geometry. Home Questions Tags Users Unanswered. Sign up using Email and Password. Is there something wrong or am I misunderstanding some stuff? Exercises from Lecture 1 ps-filepdf-file.
American Mathematical Society, I would also recommend Griffiths’s Introduction to Algebraic Curves — a beautiful text based on lectures.
Sheaf cohomology is an important technical tool. It depends partly what you are more interested in, geometry or analysis.
This is probably the approach of Forster. I will check this out. The argument is similar to the proof of Nakayama’s lemma.