Lectures on Riemann surfaces
著者
書誌事項
Lectures on Riemann surfaces
(Graduate texts in mathematics, 81)
Springer-Verlag, c1981
- : us
- : gw
- タイトル別名
-
Riemannsche Flächen
並立書誌 全1件
大学図書館所蔵 全122件
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  鳥取
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  高知
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注記
Translation of Riemannsche Flächen. Originally published as Riemannsche Flächen: Heidelberg : Springer, 1977
Bibliography: p. 243-245
Includes indexes
内容説明・目次
- 巻冊次
-
: us ISBN 9780387906171
内容説明
This book grew out of lectures on Riemann surfaces given by Otto Forster at the universities of Munich, Regensburg, and Munster. It provides a concise modern introduction to this rewarding subject, as well as presenting methods used in the study of complex manifolds in the special case of complex dimension one.
From the reviews: "This book deserves very serious consideration as a text for anyone contemplating giving a course on Riemann surfaces."--MATHEMATICAL REVIEWS
目次
1 Covering Spaces.- 1. The Definition of Riemann Surfaces.- 2. Elementary Properties of Holomorphic Mappings.- 3. Homotopy of Curves. The Fundamental Group.- 4. Branched and Unbranched Coverings.- 5. The Universal Covering and Covering Transformations.- 6. Sheaves.- 7. Analytic Continuation.- 8. Algebraic Functions.- 9. Differential Forms.- 10. The Integration of Differential Forms.- 11. Linear Differential Equations.- 2 Compact Riemann Surfaces.- 12. Cohomology Groups.- 13. Dolbeault's Lemma.- 14. A Finiteness Theorem.- 15. The Exact Cohomology Sequence.- 16. The Riemann-Roch Theorem.- 17. The Serre Duality Theorem.- 18. Functions and Differential Forms with Prescribed Principal Parts.- 19. Harmonic Differential Forms.- 20. Abel's Theorem.- 21. The Jacobi Inversion Problem.- 3 Non-compact Riemann Surfaces.- 22. The Dirichlet Boundary Value Problem.- 23. Countable Topology.- 24. Weyl's Lemma.- 25. The Runge Approximation Theorem.- 26. The Theorems of Mittag-Leffler and Weierstrass.- 27. The Riemann Mapping Theorem.- 28. Functions with Prescribed Summands of Automorphy.- 29. Line and Vector Bundles.- 30. The Triviality of Vector Bundles.- 31. The Riemann-Hilbert Problem.- A. Partitions of Unity.- B. Topological Vector Spaces.- References.- Symbol Index.- Author and Subject Index.
- 巻冊次
-
ISBN 9781461259633
内容説明
This book grew out of lectures on Riemann surfaces given by Otto Forster at the universities of Munich, Regensburg, and Munster. It provides a concise modern introduction to this rewarding subject, as well as presenting methods used in the study of complex manifolds in the special case of complex dimension one.
From the reviews: "This book deserves very serious consideration as a text for anyone contemplating giving a course on Riemann surfaces."--MATHEMATICAL REVIEWS
目次
1 Covering Spaces.- 1. The Definition of Riemann Surfaces.- 2. Elementary Properties of Holomorphic Mappings.- 3. Homotopy of Curves. The Fundamental Group.- 4. Branched and Unbranched Coverings.- 5. The Universal Covering and Covering Transformations.- 6. Sheaves.- 7. Analytic Continuation.- 8. Algebraic Functions.- 9. Differential Forms.- 10. The Integration of Differential Forms.- 11. Linear Differential Equations.- 2 Compact Riemann Surfaces.- 12. Cohomology Groups.- 13. Dolbeault's Lemma.- 14. A Finiteness Theorem.- 15. The Exact Cohomology Sequence.- 16. The Riemann-Roch Theorem.- 17. The Serre Duality Theorem.- 18. Functions and Differential Forms with Prescribed Principal Parts.- 19. Harmonic Differential Forms.- 20. Abel's Theorem.- 21. The Jacobi Inversion Problem.- 3 Non-compact Riemann Surfaces.- 22. The Dirichlet Boundary Value Problem.- 23. Countable Topology.- 24. Weyl's Lemma.- 25. The Runge Approximation Theorem.- 26. The Theorems of Mittag-Leffler and Weierstrass.- 27. The Riemann Mapping Theorem.- 28. Functions with Prescribed Summands of Automorphy.- 29. Line and Vector Bundles.- 30. The Triviality of Vector Bundles.- 31. The Riemann-Hilbert Problem.- A. Partitions of Unity.- B. Topological Vector Spaces.- References.- Symbol Index.- Author and Subject Index.
- 巻冊次
-
: gw ISBN 9783540906179
内容説明
This book grew out of lectures on Riemann surfaces given by Otto Forster at the Universities of Munich, Regensburg and Munster. It provides an introduction to the subject, as well as presenting methods used in the study of complex manifolds in the special case of complex dimension one. In the first chapter, the author considers Riemann surfaces as covering spaces, develops the pertinent basics of topology and focuses on algebraic functions. The next chapter is devoted to the theory of compact Riemann surfaces and cohomology groups, with the main classical results (including the Riemann-Roch theorem, Abel's theorem and Jacobi's inversion problem). The final section covers the Riemann mapping theorem for simply connected Riemann surfaces, and the main theorems of Behnke-Stein for non-compact Riemann surfaces (the Runge approximation theorem and the theorems of Mittag-Leffler and Weierstrass).
目次
Contents: Covering Spaces.- Compact Riemann Surfaces.- Non-compact Riemann Surfaces.- Appendix.- References.- Symbol Index.- Author and Subject Index.
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