The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

Journal of the European Mathematical Society

Full-Text PDF (168 KB) | Metadata | Table of Contents | JEMS summary
Volume 13, Issue 2, 2011, pp. 297–307
DOI: 10.4171/JEMS/253

Published online: 2010-12-15

Divisors in global analytic sets

Francesca Acquistapace[1] and A. Díaz-Cano[2]

(1) Università degli Studi di Pisa, Italy
(2) Universidad Complutense de Madrid, Spain

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.

Keywords: Real analytic sets, divisors

Acquistapace Francesca, Díaz-Cano A.: Divisors in global analytic sets. J. Eur. Math. Soc. 13 (2011), 297-307. doi: 10.4171/JEMS/253