Divisors in global analytic sets

Abstract

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,ℤ2) then the divisor Y is globally principal.