Ample Subvarieties of Algebraic Varieties

affine open algebraic De Rham algebraic varieties ample vector bundle analytic space assume base points birational cả Cartier divisor Chapter char closed subscheme closed subset codimension coherent sheaf cohomology exact sequence cohomology groups complete intersection complete non-singular variety complete scheme Corollary criterion defined denote duality effective Cartier divisor effective divisor equivalent étale example Exercise finite type finite-dimensional formal completion give global sections H¹(X H¹(Y Hartshorne Hence homomorphism hyperplane hypersurfaces induction injective integral curve invertible sheaf irreducible component isomorphism Kleiman Lef X,Y Lemma Let F line bundle linear system local cohomology locally a complete locally free sheaves Math morphism natural map neighborhood noetherian normal bundle numerical Ny/x open set projective space projective variety Proposition prove resp result Rham cohomology ring S-module Serre Serre duality sheaf F sheaf of ideals subspace subvariety Supp Suppose surjective X₁ Zariski zero