Real Algebraic and Analytic Geometry Preprint Server

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Submission: 2002, October 18.

Abstract:
We prove that any divisor $Y$ of a global analytic set $X \subset \R^n$ 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 coherent, $Y$ is locally principal, $X \setminus Y$ is not connected and $Y$ represents the zero class in ${\rm H}^{\infty}_{q-1}(X,\Z_2)$ then the divisor $Y$ is globally principal.

Mathematics Subject Classification (2000): 14P15, 32C05, 32C07.

Keywords and Phrases: real analytic, divisors.

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