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

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Abstract

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

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Acknowledgments

We thank Ciaran Meachan and David Ploog for comments. We are very grateful to the referee for many helpful comments which greatly improved the exposition. A. K. was supported by the SFB/TR 45 of the DFG (German Research Foundation). P. S. was partially financially supported by the RTG 1670 of the DFG.

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Authors and Affiliations

  1. Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK

    Andreas Krug

  2. Fachbereich Mathematik der Universität Hamburg, Bundesstraße 55, 20146, Hamburg, Germany

    Pawel Sosna

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  1. Andreas Krug
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  2. Pawel Sosna
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Correspondence to Pawel Sosna.

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Krug, A., Sosna, P. On the derived category of the Hilbert scheme of points on an Enriques surface. Sel. Math. New Ser. 21, 1339–1360 (2015). https://doi.org/10.1007/s00029-015-0178-x

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