  We continue our study of the Hodge theory of degenerations, Part I of which
covered consequences of the Decomposition Theorem and Part II of which
concerned geometric applications in the isolated singularity case. The focus
here in Part III is on concrete computations in the case of non-isolated
singularities, particularly those for which the singular locus has dimension
one. These examples are significantly more involved than in the previous parts,
and include $k$-log-canonical singularities, several specific surface
singularities (both slc and non-slc), and certain singular 5-folds arising in
the study of Feynman integrals.
