Theory and applications of holomorphic functions on algebraic varieties over arbitrary ground fields / [electronic resource] Oscar Zariski.

Includes bibliographical references.

Introduction Part I. General theory of holomorphic functions 1. Strongly holomorphic functions 2. Strongly holomorphic functions on affine 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 $\mathfrak {m}$-adic rings 9. Holomorphic functions on affine 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 $V \dashrightarrow V\circ t$ 14. Proof of the fundamental theorem in the case of the transformation $V \dashrightarrow V\circ t$ 15. Last step of the proof of the fundamental theorem: transition to the derived normal model $\overline {V\circ t}$ 16. Extension of the fundamental theorem to rational transformations 17. Reduction of the proof to a special case 18. The rational transformationt $V \dashrightarrow V\circ t$ 19. The transformation $V\circ t \dashrightarrow \overline {V\circ t}$ 20. A connectedness theorem for algebraic correspondences 21. Algebraic systems of $r$-cycles 22. Proof of the principle of degeneration

Access is restricted to licensed institutions

Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

Mode of access : World Wide Web

Description based on print version record.