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Beschreibung
This text covers Riemann surface theory from elementary aspects to the fontiers 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 varities associated with these surfaces. For this new edition, the material has been brought up-to-date, and erros have been corrected. The book should be of interest no only to pure mathematicians, but also to physicists interested in string theory and related topics.
This text covers Riemann surface theory from elementary aspects to the fontiers 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 varities associated with these surfaces. For this new edition, the material has been brought up-to-date, and erros have been corrected. The book should be of interest no only to pure mathematicians, but also to physicists interested in string theory and related topics.
Zusammenfassung
This text covers Riemann surface theory from elementary aspects to the fontiers 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 varities associated with these surfaces. For this new edition, the material has been brought up-to-date, and erros have been corrected. The book should be of interest no only to pure mathematicians, but also to physicists interested in string theory and related topics.
Inhaltsverzeichnis
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.- III. 12. Torelli's Theorem.- 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.l. Hurwitz's Theorem.- V.2. Representations of the Automorphism Group on Spaces of Differentials.- V.3. Representationof Aut M on H1(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.- VII.6. The Trisecant Formula.
Details
Erscheinungsjahr: 1991
Fachbereich: Analysis
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: Einband - fest (Hardcover)
ISBN-13: 9780387977034
ISBN-10: 0387977031
Sprache: Englisch
Einband: Gebunden
Autor: Farkas, Hershel M.
Kra, Irwin
Auflage: Second Edition 1992
Hersteller: Humana
Springer
Springer US, New York, N.Y.
Verantwortliche Person für die EU: Springer-Verlag KG, Sachsenplatz 4-6, A-1201 Wien, productsafety@springernature.com
Maße: 241 x 160 x 27 mm
Von/Mit: Hershel M. Farkas (u. a.)
Erscheinungsdatum: 23.12.1991
Gewicht: 0,746 kg
Artikel-ID: 102424796

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