2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/227343We study a natural Hodge module on the Hilbert scheme of four points on affine three-space, which categorifies the Donaldson--Thomas invariant of the Hilbert scheme. We determine the weight filtration on the Hodge module explicitly in terms of intersection cohomology complexes, and compute the E-polynomial of its cohomology. The computations make essential use of a description of the singularity of the Hilbert scheme as the degeneracy locus of the Pfaffian function.22 pagesAlgebraic Geometry14C30, 14F25, 32S40text