Franklin

Theory and applications of holomorphic functions on algebraic varieties over arbitrary ground fields / Oscar Zariski.

Author/Creator:
Zariski, Oscar, author.
Publication:
Providence, Rhode Island : American Mathematical Society, [1951]
Format/Description:
Book
1 online resource (99 p.)
Series:
Memoirs of the American Mathematical Society ; number 5.
Memoirs of the American Mathematical Society, 0065-9266 ; number 5 (1951)
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Details

Subjects:
Algebraic functions.
Form/Genre:
Electronic books.
Language:
English
Contents:
""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""
Notes:
Cover title.
Includes bibliographical references.
Description based on print version record.
ISBN:
0-8218-9994-5