### Impacto

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 |

References: | Acquistapace, F., Broglia, F.: More about signatures and approximation. Geom. Dedicata 50, 107–116 (1994) Acquistapace, F., Broglia, F., Tognoli, A.: Sulla normalizzazione degli spazi analitici reali. Boll. Un. Mat. Ital. (4) 12, 26–36 (1975) |

Deposited On: | 24 Apr 2012 11:35 |

Last Modified: | 06 Feb 2014 10:13 |

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