THE DU BOIS COMPLEX OF A HYPERSURFACE AND THE MINIMAL EXPONENT

We study the Du Bois complex Ω_Z of a hypersurface Z in a smooth complex algebraic variety in terms of its minimal exponent eα.Z/. The latter is an invariant of singularities, defined as the negative of the greatest root of the reduced Bernstein–Sato polynomial of Z, and refining the log-canonical threshold. We show that if eα.Z/ > p C 1, then the canonical morphism Ω^p_Z ! Ω^{p _}_Z is an isomorphism, where Ω^{p _}_Z is the pth associated graded piece of the Du Bois complex with respect to the Hodge filtration. On the other hand, if Z is singular and eα.Z/