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Theory and Applications of Holomorphic Functions on Algebraic Varieties over Arbitrary Ground Fields
| eBook ISBN: | 978-0-8218-9994-6 |
| Product Code: | MEMO/1/5.E |
| List Price: | $21.00 |
| MAA Member Price: | $18.90 |
| AMS Member Price: | $16.80 |
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Theory and Applications of Holomorphic Functions on Algebraic Varieties over Arbitrary Ground Fields
| eBook ISBN: | 978-0-8218-9994-6 |
| Product Code: | MEMO/1/5.E |
| List Price: | $21.00 |
| MAA Member Price: | $18.90 |
| AMS Member Price: | $16.80 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 1; 1951; 90 ppMSC: Primary 14
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Table of Contents
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Chapters
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Introduction
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Part I. General theory of holomorphic functions
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1. Strongly holomorphic functions
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2. Strongly holomorphic functions on affine models
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3. The general concept of a holomorphic function
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4. Rational holomorphic functions. Some unsolved problems
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5. Digression on algebraic points
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6. Holomorphic functions, analytical irreducibility and a connectedness criterion
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7. Analytical irreducibility and normalization
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8. Some lemmas on $\mathfrak {m}$-adic rings
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9. Holomorphic functions on affine models
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Part II. Invariance of rings of holomorphic functions under rational transformations
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10. Holomorphic functions and semi-regular birational transformations
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11. Absolute birational invariance of rings of holomorphic functions
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12. Reduction of the proof of the fundamental theorem to a special case
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13. The birational transformation $V \dashrightarrow V\circ t$
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14. Proof of the fundamental theorem in the case of the transformation $V \dashrightarrow V\circ t$
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15. Last step of the proof of the fundamental theorem: transition to the derived normal model $\overline {V\circ t}$
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16. Extension of the fundamental theorem to rational transformations
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17. Reduction of the proof to a special case
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18. The rational transformationt $V \dashrightarrow V\circ t$
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19. The transformation $V\circ t \dashrightarrow \overline {V\circ t}$
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20. A connectedness theorem for algebraic correspondences
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21. Algebraic systems of $r$-cycles
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22. Proof of the principle of degeneration
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Requests
-
Chapters
-
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
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