This text covers Riemann surface theory from elementary aspects to the frontiers of current research. Open and closed surfaces are treated with emphasis on the compact case. Basic tools are developed to describe the analytic, geometric and algebraic properties of Riemann surfaces and the Abelian varieties associated with these surfaces. Topics covered include existence of meromorphic functions, the Riemann-Roch theorem, Abel's theorem, the Jacobi inversion problem, Noether's theorem and the Reimann vanishing theorem. A ...
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This text covers Riemann surface theory from elementary aspects to the frontiers of current research. Open and closed surfaces are treated with emphasis on the compact case. Basic tools are developed to describe the analytic, geometric and algebraic properties of Riemann surfaces and the Abelian varieties associated with these surfaces. Topics covered include existence of meromorphic functions, the Riemann-Roch theorem, Abel's theorem, the Jacobi inversion problem, Noether's theorem and the Reimann vanishing theorem. A complete treatment of the uniformization of Riemann surfaces via Fuchsian groups, including branched coverings, is presented. Alternate proofs for the most important results are included, showing the diversity of approaches to the subject.
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Add this copy of Riemann Surfaces to cart. $75.14, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2012 by Springer.
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