Isolated singularities with large class group

Abstract

Let $d\ge 3$ and $g\ge 1$ be integers. Using a geometric construction involving the symmetric product of a projective curve, we exhibit a $d$-dimensional complete local normal domain over $\mathbb{C}$ with an isolated singularity such that its class group contains a copy of $(\mathbb{R}/\mathbb{Z}{)}^{\oplus 2g}$ as subgroup.

arXiv commentFormer Proposition 1.1 contained a mistake and was removed. Other results have been adjusted accordingly