Intersection Theory

a₁ assume blow-up bundle of rank c₁ canonical Cartier divisor Chern classes closed imbedding closed subscheme codim codimension coefficients coherent sheaf cohomology commutes complex construction Corollary corresponding curve cycle D₁ defined degree denoted determines diagram equation exact sequence Example exceptional divisor fibre square finite flat follows geometry given ground field Gysin homomorphisms H₁ homology hypersurfaces ideal imbedding of codimension integers intersection class intersection multiplicity intersection product intersection theory irreducible component isomorphism k-cycle Lemma Let f line bundle Math morphism f non-singular non-singular variety normal bundle normal cone polynomial projective variety proof proper morphism Proposition pull-back push-forward quasi-projective rational equivalence regular imbedding relative dimension resp Riemann-Roch ring sheaf sheaves singular smooth subvariety surjective tangent Theorem topology V₁ vector bundle X₁ Y₁ zero section