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

Author: Oscar Zariski
Publisher: Providence, R.I. : American Mathematical Society, 1951.
Series: Memoirs of the American Mathematical Society, no. 5.
Edition/Format:   Print book : EnglishView all editions and formats
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Additional Physical Format: Online version:
Zariski, Oscar, 1899-1986.
Theory and applications of holomorphic functions on algebraic varieties over arbitrary ground fields.
New York City : American Mathematical Society, 1951
(OCoLC)654394588
Document Type: Book
All Authors / Contributors: Oscar Zariski
ISBN: 082181205X 9780821812051
OCLC Number: 1251817
Description: 90 pages ; 25 cm.
Contents: Introduction --
Part I. General theory of holomorphic functions ; Strongly holomorphic functions --
Strongly holomorphic functions on affine models --
The general concept of a holomorphic function --
Rational holomorphic functions --
Digression on algebraic points --
Holomorphic functions, analytical irreducibility and a connectedness criterion --
Analytical irreducibility and normalization --
Some lemmas on [italic] m-adic rings --
Part II. Invariance of rings of holomorphic functions under rational transformations ; Holomorphic functions and semi-regular birational transformations --
Absolute birational invariance of rings of holomorphic functions --
Reduction of the proof of the fundamental theorem to a special case --
The birational transformation V--> Vot --
Last step of the proof : transition to the derived normal model Vot --
Extension of the fundamental theorem to rational transformations --
Reduction of the proof to a special case --
The rational transformation V--> Vot --
The transformation V--> V̄̄̄ōt̄ --
Part III. The principle of degeneration ; A connectedness theorem for algebraic correspondence --
Algebraic systems of cycles --
Proof of the principle of degeneration.
Series Title: Memoirs of the American Mathematical Society, no. 5.
Responsibility: by Oscar Zariski.

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