## Global Theory of Several Complex Variables: Course |

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### Contents

Frechet Sheaves | 5 |

Approximation Theorems | 14 |

h Cohomology on Complex Manifolds | 24 |

16 other sections not shown

### Common terms and phrases

algebra analytic polyhedron analytic space assume biholomorphic Choose closed submanifold coherent analytic sheaf cohomology compact connected Reinhardt compact set compact subset complex manifold connected components connected Reinhardt set continuous linear functional convex Hausdorff space convex hull coordinate bundle coordinate system Corollary Definition denote divisor domain of holomorphy Embedding Theorem exact sequence extreme point family of pseudonorms Frechet space function f Hausdorff space hence holomorphic functions holomorphic map holomorphically convex induced irreducible isomorphism Lemma Let f line bundle locally convex Hausdorff manifold of dimension meromorphic function norm Oka-Weil domain open set open subset plurisubharmonic function polynomially convex Proof pseudoconvex rational polynomials relatively compact subdomain resp restriction map Riemann domain separates points sheaf of germs sheaves Stein manifold subsheaf subvariety topology defined unit polycylinder vector bundles vector space weak topology