Geodesic
Divisors in global analytic sets
Journal of the European Mathematical Society, Tome 13 (2011) no. 2, pp. 297-307.

Voir la notice de l'article provenant de la source EMS Press

We prove that any divisor Y of a global analytic set X⊂Rn 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 Hq–1∞​(X,Z2​) then the divisor Y is globally principal.
DOI : 10.4171/jems/253
Classification : 14-XX, 32-XX, 00-XX
Keywords: Real analytic sets, divisors 
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     author = {Francesca Acquistapace and A. D{\'\i}az-Cano},
     title = {Divisors in global analytic sets},
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Francesca Acquistapace; A. Díaz-Cano. Divisors in global analytic sets. Journal of the European Mathematical Society, Tome 13 (2011) no. 2, pp. 297-307. doi : 10.4171/jems/253. http://geodesic.mathdoc.fr/articles/10.4171/jems/253/

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