## Complex analytic varieties |

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This is one of the most readable introductions to several complex variables and the geometry of complex analytic varieties. It is a shame this book is not available more widely. Whitney's exposition is excellent. I recommend reading this book to anyone wanting to know more about complex geometry and several complex variables.

### Contents

Holomorphic Functions in | 1 |

Planes projections polydisks | 3 |

Holomorphic functions in C | 4 |

Copyright | |

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### Common terms and phrases

algebraic algebraically dependent analytic in H analytic manifold analytic space Appendix biholomorphism choose clos closed coefficients compact completing the proof connected contains continuous coordinate system Corollary corresponding Cxyz defined Definition dense df(x dimpK elements equivalent Example extend finite set follows germs given gives Hausdorff space hence holds holo holomorphic extension holomorphic functions holomorphic in H holomorphic mapping holomorphic polynomial homeomorphism iffif induction integral domain intersection ircomps irreducible last lemma last theorem Lemma Lemma 4E let F linear locally analytic meromorphic functions morphic multifunction multihomogeneous neighborhood notations Note one-one open set open set H open subset plane polydisk presheaf projection proper properties prove Remark ring Section simple points smooth subvariety suppose Theorem 4A Theorem 6G topological uniquely variety vectors W-pol Weierstrass polynomial write zero set zero system