Local embeddings of lines in singular hypersurfaces Guangfeng Jiang, Dirk Siersma (1999) Annales de l'institut Fourier Lines on hypersurfaces with isolated singularities are classified. New normal forms of simple singularities with respect to lines are obtained. Several invariants are introduced.
Logarithmic embeddings of varieties with normal crossings and mixed Hodge structures. J.H.M. Steenbrink (1995) Mathematische Annalen