Theory and applications of holomorphic functions on algebraic varieties over arbitrary ground fields / Oscar Zariski.
 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, 00659266 ; number 5 (1951)  Status/Location:

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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 madic rings""; ""9. Holomorphic functions on afflne models""
""Part II: Invariance of Rings of Holomorphic Functions under Rational Transformations""""10. Holomorphic functions and semiregular 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 rcycles""; ""22. Proof of the principle of degeneration""  Notes:
 Cover title.
Includes bibliographical references.
Description based on print version record.  ISBN:
 0821899945