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, while basic tools are developed to describe the analytic, geometric, and algebraic properties of Riemann surfaces and the associated Abelian varities. Topics covered include existence of meromorphic functions, the Riemann-Roch theorem, Abel's theorem, the Jacobi inversion problem, Noether's theorem, and the Riemann vanishing theorem. A complete treatment of the uniformization of Riemann sufaces via Fuchsian groups, including branched coverings, is presented, as are alternate proofs for the most important results, showing the diversity of approaches to the subject. This title is of interest not only to pure mathematicians, but also to physicists interested in string theory and related topics.
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毕业之前要看完！ 从分析的角度，就看了里面关于单值化定理的部分。
评分oh, i can not understand it! who can tell me more about theta divisor..... HELP! I NEED HELP! what the hack is theta divisor, when we use it!
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评分毕业之前要看完！ 从分析的角度，就看了里面关于单值化定理的部分。
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