1.

Record Nr.

UNINA9910818982703321

Autore

Zariski Oscar

Titolo

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

Pubbl/distr/stampa

Providence, Rhode Island : , : American Mathematical Society, , [1951]

©1951

ISBN

0-8218-9994-5

Descrizione fisica

1 online resource (99 p.)

Collana

Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 5 (1951)

Soggetti

Algebraic functions

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Cover title.

Nota di bibliografia

Includes bibliographical references.

Nota di contenuto

""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""