A Semi-orthogonal Sequence in the Derived Category of the Hilbert Scheme of Three Points

For a smooth projective variety X of dimension d ≥ 5 over an algebraically closed field k of characteristic zero, it is shown in this paper that the bounded derived category of the Hilbert scheme of three points X[3] admits a semi-orthogonal sequence of length d-32. Each subcategory in this sequence is equivalent to the derived category of X and realized as the image of a Fourier-Mukai transform along a Grassmannian bundle G over X parametrizing planar subschemes in X[3]. The main ingredient in the proof is the computation of the normal bundle of G in X[3]. An analogous result for generalized Kummer varieties is deduced at the end.