### Francesca Acquistapace

Università degli Studi di Pisa, Italy### A. Díaz-Cano

Universidad Complutense de Madrid, Spain

We prove that any divisor $Y$ of a global analytic set $X⊂R_{n}$ 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 $H_{q–1}(X,Z_{2})$ then the divisor $Y$ is globally principal.

Francesca Acquistapace, A. Díaz-Cano, Divisors in global analytic sets. J. Eur. Math. Soc. 13 (2011), no. 2, pp. 297–307

DOI 10.4171/JEMS/253