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Journal of the European Mathematical Society


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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