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Theory and applications of holomorphic functions on algebraic varieties over arbitrary ground fields /
| Call Number: | Libro Electrónico |
|---|---|
| Main Author: | |
| Format: | Electronic eBook |
| Language: | Inglés |
| Published: |
Providence, Rhode Island :
American Mathematical Society,
[1951]
|
| Series: | Memoirs of the American Mathematical Society ;
no. 5. |
| Subjects: | |
| Online Access: | Texto completo |
Table of 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.
- 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.
- 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.