Existence and density of general components of the Noether-Lefschetz locus on normal threefolds

Abstract

We consider the Noether-Lefschetz problem for surfaces in Q-factorial normal 3-folds with rational singularities. We show the existence of components of the Noether-Lefschetz locus of maximal codimension, and that there are indeed infinitely many of them. Moreover, we show that their union is dense in the natural topology.