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

• Autore: Zariski Oscar
• Pubblicazione: Providence, Rhode Island : , : American Mathematical Society, , [1951]; ©1951
• Descrizione fisica: 1 online resource (99 p.)
• Soggetto topico: Algebraic functions
• 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""
• Titolo autorizzato: Theory and Applications of Holomorphic Functions on Algebraic Varieties over Arbitrary Ground Fields
• ISBN: 0-8218-9994-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910818982703321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society ; ; number 5.