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Record Nr. |
UNINA9910818982703321 |
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Autore |
Zariski Oscar |
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Titolo |
Theory and applications of holomorphic functions on algebraic varieties over arbitrary ground fields / / Oscar Zariski |
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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , [1951] |
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©1951 |
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ISBN |
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Descrizione fisica |
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1 online resource (99 p.) |
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Collana |
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Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 5 (1951) |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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""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 |
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