代数几何中的相交理论引论（影印版）

样章

作者：

William Fulton

定价：

67.00元

ISBN：

978-7-04-053487-0

版面字数：

160.000千字

开本：

16开

全书页数：

暂无

装帧形式：

精装

重点项目：

暂无

出版时间：

2020-04-22

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

代数几何学

暂无

preface
Chapter 1. Interseetions of Hypersurfaees
- 1.1. Early history (Bezout, Poncelet)
- 1.2. Class of a curve (Plüeker)
- 1.3. Degree of a dual surface (Salmon)
- 1.4. The problem of five conics
- 1.5. Á dynamic formula (Severi, Lazarsfeld)
- 1.6. Algebraie multiplicity, resultants
Chapter 2. Multiplicity and Normal Cones
- 2.1. Geometrie multiplicity
- 2.2. Hubert polynomials
- 2.3. Á refinement of Bezout 's theorem
- 2.4. Samuel's intersection multiplicity
- 2.5. Normal cones
- 2.6. Deformation to the normal cone
- 2.7. Intersection produets: a preview
Chapter 3. Divisors and Rational Equivalence
- 3.1. Homology and cohomology
- 3.2. Divisors
- 3.3. Rational equivalence
- 3.4. Intersecting with divisors
- 3.5. Applications
Chapter 4. Chern Classes and Segre Classes
- 4.1. Chern classes of vector bundles
- 4.2. Segre classes of cones and subvarieties
- 4.3. Intersection forumulas
Chapter 5. Gysin Maps and Intersection Rings
- 5.1. Gysin homomorphisms
- 5.2. The intersection ring of a nonsingular variety
- 5.3. Grassmannians and flag varieties
- 5.4. Enumerating tangents
Chapter 6. Degeneracy Loci
- 6.1. Á degeneracy dass
- 6.2. Schur polynomials
- 6.3. The determinantal formula
- 6.4. Symmetrie and skew-symmetric loci
Chapter 7. Refinements
- 7.1. Dynamic intersections
- 7.2. Rationality of Solutions
- 7.3. Residual intersections
- 7.4. Multiple point formulas
Chapter 8. Positivity
- 8.1. Positivity of intersection produets
- 8.2. Positive polynomials and degeneracy loci
- 8.3. Intersection multiplicities
Chapter 9. Riemann-Roch
- 9.1. The Grothendieek-Riemann-Roeh theorem
- 9.2. The singular case
Chapter 10. Miscellany
- 10.1. Topology
- 10.2. Local complete intersection morphisms
- 10.3. Contravariant and bivariant theories
- 10.4. Serre's intersection multiplieity
References
Notes (1983-1995)