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Titlebook: Riemann Surfaces; Hershel M. Farkas,Irwin Kra Textbook 19801st edition Springer Science+Business Media New York 1980 Abelian variety.Divis

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发表于 2025-3-21 16:10:26 | 显示全部楼层 |阅读模式
书目名称Riemann Surfaces
编辑Hershel M. Farkas,Irwin Kra
视频video
丛书名称Graduate Texts in Mathematics
图书封面Titlebook: Riemann Surfaces;  Hershel M. Farkas,Irwin Kra Textbook 19801st edition Springer Science+Business Media New York 1980 Abelian variety.Divis
描述The present volume is the culmination often years‘ work separately and joint­ ly. The idea of writing this book began with a set of notes for a course given by one of the authors in 1970-1971 at the Hebrew University. The notes were refined serveral times and used as the basic content of courses given sub­ sequently by each of the authors at the State University of New York at Stony Brook and the Hebrew University. In this book we present the theory of Riemann surfaces and its many dif­ ferent facets. We begin from the most elementary aspects and try to bring the reader up to the frontier of present-day research. We treat both open and closed surfaces in this book, but our main emphasis is on the compact case. In fact, Chapters III, V, VI, and VII deal exclusively with compact surfaces. Chapters I and II are preparatory, and Chapter IV deals with uniformization. All works on Riemann surfaces go back to the fundamental results of Rie­ mann, Jacobi, Abel, Weierstrass, etc. Our book is no exception. In addition to our debt to these mathematicians of a previous era, the present work has been influenced by many contemporary mathematicians.
出版日期Textbook 19801st edition
关键词Abelian variety; Divisor; Hilbert space; Jacobi; Riemann surface; Riemannsche Fläche; Surfaces; Volume; addi
版次1
doihttps://doi.org/10.1007/978-1-4684-9930-8
isbn_ebook978-1-4684-9930-8Series ISSN 0072-5285 Series E-ISSN 2197-5612
issn_series 0072-5285
copyrightSpringer Science+Business Media New York 1980
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发表于 2025-3-21 21:42:19 | 显示全部楼层
Existence Theorems,nt meromorphic functions. We do so by constructing certain harmonic differentials (with singularities). From the existence of harmonic differentials, it is trivial to construct meromorphic differentials. A ratio of two linearly independent meromorphic differentials produces a non-constant meromorphic function.
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Compact Riemann Surfaces,important theorems concerning compact Riemann surfaces : the RiemannRoch theorem, Abel’s theorem, and the Jacobi inversion theorem. Many applications of these theorems are obtained; and the simplest compact Riemann surfaces, the hyperelliptic ones, are discussed in great detail.
发表于 2025-3-22 07:12:07 | 显示全部楼层
Theta Functions, the Jacobian variety of a compact surface, and via the embedding of the Riemann surface into its Jacobian variety, multivalued holomorphic functions on the surface. The high point of our present development is the Riemann vanishing theorem (Theorem VI.3.5). Along the way, we will reprove the Jacobi inversion theorem.
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Riemann Surfaces978-1-4684-9930-8Series ISSN 0072-5285 Series E-ISSN 2197-5612
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Uniformization,This chapter has two purposes. The first and by far the most important is to prove the uniformization theorem for Riemann surfaces. This theorem describes all simply connected Riemann surfaces and hence with the help of topology, all Riemann surfaces.
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,Automorphisms of Compact Surfaces — Elementary Theory,In this chapter we develop the basic results on the automorphism group of a compact Riemann surface, continuing the study began in III.7. Some of the deeper results will have to await the creation of more powerful machinery.
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https://doi.org/10.1007/978-1-4684-9930-8Abelian variety; Divisor; Hilbert space; Jacobi; Riemann surface; Riemannsche Fläche; Surfaces; Volume; addi
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