Preface
Chapter 1.Intersections of Hypersurfaces
1.1.Early history (Bezout,Poncelet)
1.2.Class of a curve (Plicker)
1.3.Degree of a dual surface (Salmon)
1.4.The problem of five conics
1.5.A dynamic formula (Severi,Lazarsfeld)
1.6.Algebraic multiplicity,resultants
Chapter 2.Multiplicity and Normal Cones
2.1.Geometric multiplicity
2.2.Hilbert polynomials
2.3.A 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 products: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.A degeneracy class
6.2.Schur polynomials
6.3.The determinantal formula
6.4.Symmetric 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 products
8.2.Positive polynomials and degeneracy loci
8.3.Intersection multiplicities
Chapter 9.Riemann-Roch
9.1.The Grothendieck-Riemann-Roch 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 multiplicity
References
Notes(1983-1995)