The splitting principle and singularities (Q2895549)

The author expands on a meta principle \textit{Morphisms in a derived category do not split accidentally}. While the main result is a bit technical, one of the consequences is the following:NEWLINENEWLINEKollár--Kovaćs DB criterion: Let \(f:Y\to X\) be a proper morphism between reduced schemes of finite type over the complex numbers, let \(W\subset X\) an arbitrary subscheme, and \(F=f^{-1}(W)\), equipped with the induced reduced subscheme structure. Assume that the natural map \(I_{W/X}\to \mathcal{R}f_*(I_{F/Y})\) admits a left inverse. Then, if \((Y,F)\) is a Du Bois pair, so is \((X,W)\).NEWLINENEWLINEFor the entire collection see [Zbl 1236.14001].