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...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Oxford ; New York :
Oxford University Press,
2011.
|
| Schriftenreihe: | Oxford graduate texts in mathematics ;
22. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (xiii, 286 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 282-283) and index. |
| ISBN: | 9780191545849 0191545848 1299990290 9781299990296 |
Internformat
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 | ||
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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. | |
| 650 | 0 | |a Riemann surfaces. |0 http://id.loc.gov/authorities/subjects/sh85114044 | |
| 650 | 6 | |a Surfaces de Riemann. | |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn861200296 |
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| _version_ | 1816882247919206401 |
| adam_text | |
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| author | Donaldson, S. K. |
| author_facet | Donaldson, S. K. |
| author_role | |
| author_sort | Donaldson, S. K. |
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| callnumber-first | Q - Science |
| callnumber-label | QA333 |
| callnumber-raw | QA333 .D66 2011eb |
| callnumber-search | QA333 .D66 2011eb |
| callnumber-sort | QA 3333 D66 42011EB |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | 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. 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. 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. 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. |
| ctrlnum | (OCoLC)861200296 |
| dewey-full | 515.9/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.9/3 |
| dewey-search | 515.9/3 |
| dewey-sort | 3515.9 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn861200296 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:35Z |
| institution | BVB |
| isbn | 9780191545849 0191545848 1299990290 9781299990296 |
| language | English |
| oclc_num | 861200296 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xiii, 286 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Oxford University Press, |
| record_format | marc |
| series | Oxford graduate texts in mathematics ; |
| series2 | Oxford graduate texts in mathematics ; |
| spelling | Donaldson, S. K. Riemann surfaces / Simon Donaldson. Oxford ; New York : Oxford University Press, 2011. 1 online resource (xiii, 286 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Oxford graduate texts in mathematics ; 22 Includes bibliographical references (pages 282-283) and index. Print version record. 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. 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. 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. 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. 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. Riemann surfaces. http://id.loc.gov/authorities/subjects/sh85114044 Surfaces de Riemann. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Riemann surfaces fast Riemannsche Fläche gnd http://d-nb.info/gnd/4049991-1 Print version: Donaldson, S.K. Riemann surfaces 9780198526391 (DLC) 2011283705 (OCoLC)694832814 Oxford graduate texts in mathematics ; 22. http://id.loc.gov/authorities/names/n96121759 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=650774 Volltext |
| spellingShingle | Donaldson, S. K. Riemann surfaces / Oxford graduate texts in mathematics ; 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. 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. 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. 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. Riemann surfaces. http://id.loc.gov/authorities/subjects/sh85114044 Surfaces de Riemann. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Riemann surfaces fast Riemannsche Fläche gnd http://d-nb.info/gnd/4049991-1 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85114044 http://d-nb.info/gnd/4049991-1 |
| title | Riemann surfaces / |
| title_auth | Riemann surfaces / |
| title_exact_search | Riemann surfaces / |
| title_full | Riemann surfaces / Simon Donaldson. |
| title_fullStr | Riemann surfaces / Simon Donaldson. |
| title_full_unstemmed | Riemann surfaces / Simon Donaldson. |
| title_short | Riemann surfaces / |
| title_sort | riemann surfaces |
| topic | Riemann surfaces. http://id.loc.gov/authorities/subjects/sh85114044 Surfaces de Riemann. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Riemann surfaces fast Riemannsche Fläche gnd http://d-nb.info/gnd/4049991-1 |
| topic_facet | Riemann surfaces. Surfaces de Riemann. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Riemann surfaces Riemannsche Fläche |
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| work_keys_str_mv | AT donaldsonsk riemannsurfaces |