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Basic Algebraic Geometry 1

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概要 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 clear geometrical picture with cumbersome algebraic apparatus. The 15 years that have elapsed since the first edition have seen the appear ance of many beautiful books treating various branches of algebraic geometry. However, as far as I know, no other author has been attracted to the aim which this book set itself: to give an overall view of the many varied aspects of algebraic geometry, without going too far afield into the different theories. There is thus scope for a second edition. In preparing this, I have included some additional material, rather varied in nature, and have made some small cuts, but the general character of the book remains unchanged.続きを見る
目次 I. Basic Notions
1. Algebraic Curves in the Plane
Exercises to {sect}1
2. Closed Subsets of Affine Space
Exercises to {sect}2
3. Rational Functions
Exercises to {sect}3
4. Quasiprojective Varieties
Exercises to {sect}4
5. Products and Maps of Quasiprojective Varieties
Exercises to {sect}5
6. Dimension
Exercises to {sect}6
II. Local Properties
1. Singular and Nonsingular Points
Exercises to {sect}1
2. Power Series Expansions
Exercises to {sect}2
Exercises to {sect}3
4. The Structure of Birational Maps
Exercises to {sect}4
5. Normal Varieties
Exercises to {sect}5
6. Singularities of a Map
Exercises to {sect}6
III. Divisors and Differential Forms
1. Divisors
Exercises to {sect}1
2. Divisors on Curves
Exercises to {sect}2
3. The Plane Cubic
Exercises to {sect}3
4. Algebraic Groups
Exercises to {sect}4
5. Differential Forms
Exercises to {sect}5
6. Examples and Applications of Differential Forms
Exercises to {sect}6
IV. Intersection Numbers
1. Definition and Basic Properties
Exercises to {sect}1
2. Applications of Intersection Numbers
Exercises to {sect}2
3. Birational Maps of Surfaces
Exercises to {sect}3
4. Singularities
Exercises to {sect}4
Algebraic Appendx
References.
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登録日 2020.06.27
更新日 2021.05.09

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