俄羅斯數學經典-沙法列維奇代數幾何基礎教程 (第1卷) (第3版) 9787519296636 (俄)I.R.Shafa

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書名:俄羅斯數學經典-沙法列維奇代數幾何基礎教程 (第1卷) (第3版)
ISBN:9787519296636
出版社:世界圖書出版公司
著編譯者:(俄)I.R.Shafarevich
頁數:310
所在地:中國大陸 *此為代購商品
書號:1556490
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【台灣高等教育出版社簡體書】 俄羅斯數學經典-沙法列維奇代數幾何基礎教程 (第1卷) (第3版) 787519296636 (俄)I.R.Shafarevich

內容簡介

本書是沙法列維奇代數幾何基礎教程的第1卷。本書作者沙法列維奇是當代著名數學家,被譽為蘇聯數學三巨頭之一,他建立了為世人矚目的蘇聯代數幾何和代數數論學派。他的代數幾何基礎教程(俄文版1972年初版,英文版1977年初版)問世五十多年來,歷經三版修訂,一直被視為一部重要的代數幾何經典名著。與同類教材相比,該教程內容全面詳盡,注重給出抽象理論的幾何背景和起源,並配有充分反映幾何本質的實例和圖解。本書所需預備知識僅限於代數基礎,是高年級本科生和研究生學習代數幾何的首選教材。該教程的第3版分為兩卷,第1卷討論射影空間中的簇,第2卷討論概形和複流形。

目錄

Book 1: Varieties in Projective Space
1 Basic Notions
1 Algebraic Curves in the Plane
1 1 Plane Curves
1 2 Rational Curves
1 3 Relation with Field Theory
1 4 Rational Maps
1 5 Singular and Nonsingular Points
1 6 The Projective Plane
1 7 Exercises to Section 1
2 Closed Subsets of Affine Space
2 1 Definition of Closed Subsets
2 2 Regular Functions on a Closed Subset
2 3 Regular Maps
2 4 Exercises to Section 2
3 Rational Functions
3 1 Irreducible Algebraic Subsets
3 2 Rational Functions
3 3 Rational Maps
3 4 Exercises to Section 3
4 Quasiprojective Varieties
4 1 Closed Subsets of Projective Space
4 2 Regular Functions
4 3 Rational Functions
4 4 Examples of Regular Maps
4 5 Exercises to Section 4
5 Products and Maps of Quasiprojective Varieties
5 1 Products
5 2 The Image of a Projective Variety is Closed
5 3 Finite Maps
5 4 Noether Normalisation
5 5 Exercises to Section 5
6 Dimension
6 1 Definition of Dimension
6 2 Dimension of Intersection with a Hypersurface
6 3 The Theorem on the Dimension of Fibres
6 4 Lines on Surfaces
6 5 Exercises to Section 6
2 Local Properties
1 Singular and Nonsingular Points
1 1 The Local Ring of a Point
1 2 The Tangent Space
1 3 Intrinsic Nature of the Tangent Space
1 4 Singular Points
1 5 The Tangent Cone
1 6 Exercises to Section 1
2 Power Series Expansions
2 1 Local Parameters at a Point
2 2 Power Series Expansions
2 3 Varieties over the Reals and the Complexes
2 4 Exercises to Section 2
3 Properties of Nonsingular Points
3 1 Codimension 1 Subvarieties
3 2 Nonsingular Subvarieties
3 3 Exercises to Section 3
4 The Structure of Birational Maps
4 1 Blowup in Projective Space
4 2 Local Blowup
4 3 Behaviour of a Subvariety Under a Blowup
4 4 Exceptional Subvarieties
4 5 Isomorphism and Birational Equivalence
4 6 Exercises to Section 4
5 Normal Varieties
5 1 Normal Varieties
5 2 Normalisation of an Affine Variety
5 3 Normalisation of a Curve
5 4 Projective Embedding of Nonsingular Varieties
5 5 Exercises to Section 5
6 Singularities of a Map
6 1 Irreducibility
6 2 Nonsingularity
6 3 Ramification
6 4 Examples
6 5 Exercises to Section 6

Book 2: Schemes and Varieties
Book 3: Complex Algebraic Varieties and Complex Manifolds

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