Du Bois property
Hodge theory of smooth projective varieties is a very powerful tool. For many applications the most important piece is the surjectivity of the natural map
This surjectivity continues to hold for certain mildly singular varieties. Steenbrink identified the correct class and dubbed them Du Bois singularities.
One should think of Du Bois as a weakening of rationality. If a pair (X, Δ) is dlt then X has rational singularities (2.88). If (X, Δ) is lc or slc, in general it does not have rational singularities, but we prove in (6.32) that X is Du Bois.
A crucial advantage of the concept of Du Bois singularities is that, on the one ...