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

版面字数：

160千字

开本：

16开

装帧形式：

精装

版次：

最新版次
印刷时间：

2023年

ISBN：

978-7-04-053487-0

物料号：

53487-00

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

目录
- 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)