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

## TL;DR

This paper investigates the structure of the Noether-Lefschetz locus on certain normal threefolds, proving the existence of infinitely many dense components of maximal codimension.

## Contribution

It establishes the existence, density, and infinitude of components of the Noether-Lefschetz locus on Q-factorial normal threefolds with rational singularities.

## Key findings

- Existence of maximal codimension components
- Infinitely many such components exist
- Their union is dense in the natural topology

## 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.