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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Sheaf cohomology is an important technical tool. The Runge Approximation Theorem.
Lectures on Riemann Surfaces
Home Questions Tags Users Unanswered. I do recommend riemannn recent published book by Donaldson on this subject. I enjoyed Erik Reyssat’s book in the Progress in Mathematics series for it balance between clarity and concision. Xuxu 2 8.
Personally I found the following survey article very inspiring when learning the subject: The more analytic approach is to begin with compact complex one manifolds and prove they are all representable as algebraic curves. Perspectives on Riemann Surfaces.
I found that argument confusing too. 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 sutfaces algebraic constructions they will see in more generality later I think Elements of Algebra John Stillwell.
Email Required, but never shown. Mumford’s book Complex projective varieties I, also has a terrific chapter on curves from the complex analytic point of view. Dispatched from the UK in 1 business day When will my order arrive?
I recommend “Lectures on Riemann Surfaces” by Forster. The Exact Cohomology Sequence. Abel-Jacobi theorem and its first corollaries. But only the first cohomology groups are used and these are comparatively easy to handle. Meromorphic functions on complex tori. There are many good references.
Forster: Riemann Surfaces
Exercises from Lecture 9 ps-filepdf-file. Meromorphic functions, first properties of morhisms of Riemann surfaces. Line suraces Vector Bundles. Post as a guest Name.
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? Take everything on 1 to one side and multiply by the adjugate matrix.
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. Sign up or log in Sign up using Google. I’d say they’re about equal in difficulty level and comprehensibility, but you might have a different opinion.
Lectures on Riemann Surfaces – Otto Forster – Google Books
The Jacobi Inversion Problem. Home Questions Tags Users Unanswered. The Universal Covering and Covering Transformations. How should I understand this theorem? The argument is similar to the proof of Nakayama’s lemma.