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Divisors in global analytic sets

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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Official URL: http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=13&iss=2&rank=2&srch=searchterm%7CDivisors+in+global+analytic+sets

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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
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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