The Milnor fibre of the Pfaffian and the Hilbert scheme of four points on~$\C^3$

begin{abstract} We 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.

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Published 1 January 2009