A semi-orthogonal sequence in the derived category of the Hilbert scheme of three points

Abstract For a smooth and quasi-projective variety X of dimension d 5 d ≥ 5 over an algebraically closed field k of characteristic zero, it is shown in this paper that the bounded derived category {\, Dᵇ\, } (X^3) D b (X 3) of the Hilbert scheme of three points admits a semi-orthogonal sequence of length (array{cd-3\\ 2array}) d - 3 2. Each subcategory in this sequence is equivalent to {\, Dᵇ\, } (X) D b (X) and realized as the image of a Fourier–Mukai transform along a Grassmannian bundle G X G → X parametrizing planar subschemes in X^3 X 3. The main ingredient in the proof is the computation of the normal bundle of G G in X^3 X 3. An analogous result for generalized Kummer varieties is deduced at the end.