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On bertini-type theorem for weakly-normal complex analytic sets.
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| Abstract | Introduction. The aim of the paper is to present an elementary proof of the following Bertini-type theorem for weakly-normal complex analytic sets Theorem 1. If X is a weakly-normal locally analytic subset of C n then there exists a fat subset M of the space of all affine hyperplanes in C n such that for every H 2 M the intersection X " H is again weakly-normal. In [M, Corollary II.6] an analogous Bertini-type theorem for normal and reduced locally analytic sets in C n is proved. Proofs for normal and reduced complex analytic sets are very similar, a Bertini-type theorem is deduced from two facts: a Sard-type theorem and the openness condition for the given property. In [M1, Thm. 18.] Manaresi proved that this kind of arguments may be applied to any local property of complex spaces (not |
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| Subject Keyword | Bertini-type Theorem Weakly-normal Complex Analytic Set Analytic Set Analytic Subset Following Bertini-type Theorem Elementary Proof Affine Hyperplanes Local Property Fat Subset Openness Condition Analogous Bertini-type Theorem Complex Space Sard-type Theorem Corollary Ii Reduced Complex Analytic Set |
| Content Type | Text |
