代数几何中的相交理论引论(影印版)

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)