| Description |
1 online resource (99 pages) |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; number 5 (1951) |
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Memoirs of the American Mathematical Society ; no. 5.
|
| Contents |
Introduction -- Part I: General Theory of Holomorphic Functions -- 1. Strongly holomorphic functions -- 2. Strongly holomorphic functions on afflne models -- 3. The general concept of a holomorphic function -- 4. Rational holomorphic functions. Some unsolved problems -- 5. Digression on algebraic points -- 6. Holomorphic functions, analytical irreducibility and a connectedness criterion -- 7. Analytical Irreducibility and normalization -- 8. Some lemmas on m-adic rings -- 9. Holomorphic functions on afflne models |
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Part II: Invariance of Rings of Holomorphic Functions under Rational Transformations -- 10. Holomorphic functions and semi-regular birational transformations -- 11. Absolute birational Invariance of rings of holomorphic functions -- 12. Reduction of the proof of the fundamental theorem to a special case -- 13. The birational transformation V --> Vot -- 14. Proof of the fundamental theorem in the case of the transformation V --> Vot -- 15. Last step of the proof of the fundamental theorem: transition to the derived normal model Vot |
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16. Extension of the fundamental theorem to rational transformations -- 17. Reduction of the proof to a special case -- 18. The rational transformation V --> Vot -- 19. The transformation Vot --> Vot -- Part III: The Principle of Degeneration -- 20. A connectedness theorem for algebraic correspondences -- 21. Algebraic systems of r-cycles -- 22. Proof of the principle of degeneration |
| Notes |
Cover title |
| Bibliography |
Includes bibliographical references |
| Notes |
English |
|
Print version record |
| Subject |
Algebraic functions.
|
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Algebraic functions
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| Form |
Electronic book
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| ISBN |
9780821899946 |
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0821899945 |
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