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We use semi-orthogonal decompositions to construct autoequivalences ofHilbert schemes of points on Enriques surfaces and of Calabi-Yau varietieswhich cover them. While doing this, we show that the derived category of asurface whose irregularity and geometric genus vanish embeds into the derivedcategory of its Hilbert scheme of points.

On the derived category of the Hilbert scheme of points on an Enriques surface