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Acquistapace, Francesca and Díaz-Cano Ocaña, Antonio
(2011)
*Divisors in global analytic sets.*
Journal of the European Mathematical Society, 13
(2).
pp. 297-307.
ISSN 1435-9855

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## Abstract

We prove that any divisor Y of a global analytic set X subset of R(n) has a generic equation, that is, there is an analytic function vanishing on Y with multiplicity one along each irreducible component of Y. We also prove that there are functions with arbitrary multiplicities along Y. The main result states that if X is pure dimensional, Y is locally principal, X \ Y is not connected and Y represents the zero class in H(q-1)(infinity) (X, Z(2)) then the divisor Y is globally principal.

Item Type: | Article |
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Uncontrolled Keywords: | Real analytic sets; Divisors |

Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 14977 |

Deposited On: | 24 Apr 2012 11:35 |

Last Modified: | 02 Aug 2018 08:35 |

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