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[null,"1.","Record Nr.",null,"UNINA9910818982703321"]
[null,null,"Autore",null,"Zariski Oscar"]
[null,null,"Titolo",null,"Theory and applications of holomorphic functions on algebraic varieties over arbitrary ground fields / / Oscar Zariski"]
[null,null,"Pubbl/distr/stampa",null,"Providence, Rhode Island : , : American Mathematical Society, , [1951]"]
[{"$nulls":4},"©1951"]
[null,null,"ISBN",null,"0-8218-9994-5"]
[null,null,"Descrizione fisica",null,"1 online resource (99 p.)"]
[null,null,"Collana",null,"Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 5 (1951)"]
[null,null,"Soggetti",null,"Algebraic functions"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Cover title."]
[null,null,null,"Nota di bibliografia","Includes bibliographical references."]
[null,null,"Nota di contenuto",null,"\"\"Contents\"\"; \"\"Introduction\"\"; \"\"Part I: General Theory of Holomorphic Functions\"\"; \"\"1. Strongly holomorphic functions\"\"; \"\"2. Strongly holomorphic functions on afflne models\"\"; \"\"3. The general concept of a holomorphic function\"\"; \"\"4. Rational holomorphic functions. Some unsolved problems\"\"; \"\"5. Digression on algebraic points\"\"; \"\"6. Holomorphic functions, analytical irreducibility and a connectedness criterion\"\"; \"\"7. Analytical Irreducibility and normalization\"\"; \"\"8. Some lemmas on m-adic rings\"\"; \"\"9. Holomorphic functions on afflne models\"\""]
[{"$nulls":4},"\"\"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\"\""]
[{"$nulls":4},"\"\"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\"\""]