最 低 价：￥614.70
| BOOK 1. Varieties in projective space Chapter I. 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 Exercises to 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 Exercises to 2 3. Rational Functions 3.1. Irreducible Algebraic Subsets 3.2. Rational Functions 3.3. Rational Maps Exercises to 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 Exercises to 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 Exercises to 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 Exercises to 6 Chapter II. 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 Exercises to 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 Exercises to 2 3. Properties of Nonsingular Points 3.1. Codimension 1 Subvarieties 3.2. Nonsingular Subvarieties Exercises to 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 Exercises to 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 Exercises to 5 6. Singularities of a Map 6.1. Irreducibility 6.2. Nonsingularity 6.3. Ramification 6.4. Examples Exercises to 6 Chapter III Divisors and differential forms Chapter iv:Intersecction numbers Algebraic appendix References Index BOOK 2. Schemes and varieties Chapter v Schemes Chapter vi Varieties BOOK 3 Complex algebraic varieties and complex manifolds Chapter vii The topology of algebraic varieties Chapter viii Complex manifolds Chapter IX Universal cover Historical sketch References Index |
内容加载中，请稍后...
商品评论（0条）