Riemann Surfaces / by Hershel M. Farkas, Irwin Kra
(Graduate Texts in Mathematics ; 71)
| データ種別 | 電子ブック |
|---|---|
| 出版者 | New York, NY : Springer New York : Imprint: Springer |
| 出版年 | 1980 |
| 本文言語 | 英語 |
| 大きさ | XI, 340 p : online resource |
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| 内容注記 | 0 An Overview 0.1 Topological Aspects, Uniformization, and Fuchsian Groups 0.2 Algebraic Functions 0.3. Abelian Varieties 0.4. More Analytic Aspects I Riemann Surfaces I.1. Definitions and Examples I.2. Topology of Riemann Surfaces I.3. Differential Forms I.4. Integration Formulae II Existence Theorems II.1. Hilbert Space Theory—A Quick Review II.2. Weyl’s Lemma II.3. The Hilbert Space of Square Integrable Forms II.4. Harmonic Differentials II.5. Meromorphic Functions and Differentials III Compact Riemann Surfaces III.1. Intersection Theory on Compact Surfaces III.2. Harmonic and Analytic Differentials on Compact Surfaces III.3. Bilinear Relations III.4. Divisors and the Riemann—Roch Theorem III.5. Applications of the Riemann—Roch Theorem III.6. Abel’s Theorem and the Jacobi Inversion Problem III.7. Hyperelliptic Riemann Surfaces III.8. Special Divisors on Compact Surfaces III.9. Multivalued Functions III.10. Projective Imbeddings III.11. More on the Jacobian Variety IV Uniformization IV.1. More on Harmonic Functions (A Quick Review) IV.2. Subharmonic Functions and Perron’s Method IV.3. A Classification of Riemann Surfaces IV.4. The Uniformization Theorem for Simply Connected Surfaces IV.5. Uniformization of Arbitrary Riemann Surfaces IV.6. The Exceptional Riemann Surfaces IV.7. Two Problems on Moduli IV.8. Riemannian Metrics IV.9. Discontinuous Groups and Branched Coverings IV.10. Riemann–Roch—An Alternate Approach IV.11. Algebraic Function Fields in One Variable V Automorphisms of Compact Surfaces Elementary Theory V.1. Hurwitz’s Theorem V.2. Representations of the Automorphism Group on Spaces of Differentials V.3. Representations of Aut M on H>1(M) V.4. The Exceptional Riemann Surfaces VI Theta Functions VI.1. The Riemann Theta Function VI.2. The Theta Functions Associated with a Riemann Surface VI.3. The Theta Divisor VII Examples VII.1. Hyperelliptic Surfaces (Once Again) VII.2. Relations among Quadratic Differentials VII.3. Examples of Non-hyperelliptic Surfaces VII.4. Branch Points of Hyperelliptic Surfaces as Holomorphic Functions of the Periods VII.5. Examples of Prym Differentials |
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| 一般注記 | 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 |
| 著者標目 | *Farkas, Hershel M. author Kra, Irwin author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Algebraic geometry LCSH:Mathematical analysis LCSH:Analysis (Mathematics) FREE:Mathematics FREE:Analysis FREE:Algebraic Geometry |
| 分 類 | DC23:515 |
| 巻冊次 | ISBN:9781468499308 
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| ISBN | 9781468499308 |
| URL | http://dx.doi.org/10.1007/978-1-4684-9930-8 |
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