Basic Algebraic Geometry 1
The first edition of this book came out just as the apparatus of algebraic geometry was reaching a stage that permitted a lucid and concise account of the foundations of the subject. The author was no longer forced into the painful choice between sacrificing rigour of exposition or overloading the c...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
1994, 1994
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| Edition: | 2nd ed. 1994 |
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| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- I. Basic Notions
- 1. Algebraic Curves in the Plane
- Exercises to §1
- 2. Closed Subsets of Affine Space
- Exercises to §2
- 3. Rational Functions
- Exercises to §3
- 4. Quasiprojective Varieties
- Exercises to §4
- 5. Products and Maps of Quasiprojective Varieties
- Exercises to §5
- 6. Dimension
- Exercises to §6
- II. Local Properties
- 1. Singular and Nonsingular Points
- Exercises to §1
- 2. Power Series Expansions
- Exercises to §2
- Exercises to §3
- 4. The Structure of Birational Maps
- Exercises to §4
- 5. Normal Varieties
- Exercises to §5
- 6. Singularities of a Map
- Exercises to §6
- III. Divisors and Differential Forms
- 1. Divisors
- Exercises to §1
- 2. Divisors on Curves
- Exercises to §2
- 3. The Plane Cubic
- Exercises to §3
- 4. Algebraic Groups
- Exercises to §4
- 5. Differential Forms
- Exercises to §5
- 6. Examples and Applications of Differential Forms
- Exercises to §6
- IV. Intersection Numbers
- 1. Definition and Basic Properties
- Exercises to §1
- 2. Applications of Intersection Numbers
- Exercises to §2
- 3. Birational Maps of Surfaces
- Exercises to §3
- 4. Singularities
- Exercises to §4
- Algebraic Appendx
- References