Pluripolar hulls and fine analytic structure

Abstract

We discuss the relation between pluripolar hulls and fine analytic structure. Our main result is the following. For each non polar subset $S$ of the complex plane $\mathbb{C}$ we prove that there exists a pluripolar set $E\subset (S\times \mathbb{C})$ with the property that the pluripolar hull of $E$ relative to ${\mathbb{C}}^2$ contains no fine analytic structure and its projection onto the first coordinate plane equals $\mathbb{C}$.

14 pages, revised version, to appear in Indagationes Mathematicae