## Lecture Notes in Mathematics, Volume 156 |

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### Contents

Formalrational functions along a subvariety | 20 |

Affine open subsets | 59 |

Generalization to higher codimensions | 81 |

Copyright | |

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affine open affine scheme ample vector bundle analytic space assume base points birational blowing-up Cartier divisor Chapter char closed subscheme closed subset codimension coherent sheaf cohomology exact sequence complete curves complete intersection complete non-singular variety complete scheme complete variety completes the proof Corollary define denote duality effective ample divisor effective divisor eorem equivalent ercise Exercise finite type finite-dimensional free sheaf global sections Grothendieck LC Hartshorne Hence homomorphism hypersurfaces induction injective integral curve invertible sheaf irreducible component isomorphism Kleiman Lef X,Y lemma Let f line bundle linear system locally free sheaves morphism natural map noetherian non-singular subvariety non-singular surface normal bundle open set open subset projective space Proposition 3.1 prove resp result Rham cohomology ring S,pr Seiten Serre set-theoretic complete intersection sheaf F sheaf of ideals subspace subvariety Supp Suppose surjective variety of dimension vector space zero