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)