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.

中文翻译：

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Noether-Lefschetz 轨迹在正态三重上的一般分量的存在性和密度

我们考虑具有有理奇点的 Q 阶乘法向 3 倍曲面的 Noether-Lefschetz 问题。我们证明了最大余维的 Noether-Lefschetz 轨迹的分量的存在，并且确实存在无穷多个分量。此外，我们表明它们的联合在自然拓扑中是密集的。