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Riemann surfaces /
This is an authoritative but accessible text on one dimensional complex manifolds or Riemann surfaces. Dealing with the main results on Riemann surfaces from a variety of points of view the book pulls together materials from global analysis topology, and algebraic geometry, and covers the essential...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford ; New York :
Oxford University Press,
2011.
|
| Colección: | Oxford graduate texts in mathematics ;
22. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Donaldson, S. K. | |
| 245 | 1 | 0 | |a Riemann surfaces / |c Simon Donaldson. |
| 264 | 1 | |a Oxford ; |a New York : |b Oxford University Press, |c 2011. | |
| 300 | |a 1 online resource (xiii, 286 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a Oxford graduate texts in mathematics ; |v 22 | |
| 504 | |a Includes bibliographical references (pages 282-283) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | 8 | |a This is an authoritative but accessible text on one dimensional complex manifolds or Riemann surfaces. Dealing with the main results on Riemann surfaces from a variety of points of view the book pulls together materials from global analysis topology, and algebraic geometry, and covers the essential mathematical methods and tools. | |
| 505 | 0 | |a Cover; Contents; PART I: PRELIMINARIES; 1 Holomorphic functions; 1.1 Simple examples: algebraic functions; 1.2 Analytic continuation: differential equations; Exercises; 2 Surface topology; 2.1 Classification of surfaces; 2.2 Discussion: the mapping class group; Exercises; PART II: BASIC THEORY; 3 Basic definitions; 3.1 Riemann surfaces and holomorphic maps; 3.2 Examples; Exercises; 4 Maps between Riemann surfaces; 4.1 General properties; 4.2 Monodromy and the Riemann Existence Theorem; Exercises; 5 Calculus on surfaces; 5.1 Smooth surfaces; 5.2 de Rham cohomology. | |
| 505 | 8 | |a 5.3 Calculus on Riemann surfacesExercises; 6 Elliptic functions and integrals; 6.1 Elliptic integrals; 6.2 The Weierstrass [Omitted] function; 6.3 Further topics; Exercises; 7 Applications of the Euler characteristic; 7.1 The Euler characteristic and meromorphic forms; 7.2 Applications; Exercises; PART III: DEEPER THEORY; 8 Meromorphic functions and the Main Theorem for compact Riemann surfaces; 8.1 Consequences of the Main Theorem; 8.2 The Riemann-Roch formula; Exercises; 9 Proof of the Main Theorem; 9.1 Discussion and motivation; 9.2 The Riesz Representation Theorem. | |
| 505 | 8 | |a 9.3 The heart of the proof9.4 Weyl's Lemma; Exercises; 10 The Uniformisation Theorem; 10.1 Statement; 10.2 Proof of the analogue of the Main Theorem; Exercises; PART IV: FURTHER DEVELOPMENTS; 11 Contrasts in Riemann surface theory; 11.1 Algebraic aspects; 11.2 Hyperbolic surfaces; Exercises; 12 Divisors, line bundles and Jacobians; 12.1 Cohomology and line bundles; 12.2 Jacobians of Riemann surfaces; Exercises; 13 Moduli and deformations; 13.1 Almost-complex structures, Beltrami differentials and the integrability theorem; 13.2 Deformations and cohomology; 13.3 Appendix; Exercises. | |
| 505 | 8 | |a 14 Mappings and moduli14.1 Diffeomorphisms of the plane; 14.2 Braids, Dehn twists and quadratic singularities; 14.3 Hyperbolic geometry; 14.4 Compactification of the moduli space; Exercises; 15 Ordinary differential equations; 15.1 Conformal mapping; 15.2 Periods of holomorphic forms and ordinary differential equations; Exercises; References; Index; A; B; C; D; E; F; G; H; I; J; K; L; M; N; O; P; Q; R; S; T; U; V; W. | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Riemann surfaces. | |
| 650 | 6 | |a Surfaces de Riemann. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Riemann surfaces. |2 fast |0 (OCoLC)fst01097801 | |
| 650 | 7 | |a Riemannsche Fläche |2 gnd | |
| 776 | 0 | 8 | |i Print version: |a Donaldson, S.K. |t Riemann surfaces |z 9780198526391 |w (DLC) 2011283705 |w (OCoLC)694832814 |
| 830 | 0 | |a Oxford graduate texts in mathematics ; |v 22. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=650774 |z Texto completo |
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