Mathematische Annalen

, Volume 365, Issue 1–2, pp 155–172 | Cite as

Derived equivalent Calabi–Yau threefolds from cubic fourfolds

  • John R. CalabreseEmail author
  • Richard P. Thomas


We describe pretty examples of derived equivalences and autoequivalences of Calabi-Yau threefolds arising from pencils of cubic fourfolds. The cubic fourfolds are chosen to be special, so they each have an associated K3 surface. Thus a pencil gives rise to two different Calabi-Yau threefolds: the associated pencil of K3 surfaces, and the baselocus of the original pencil—the intersection of two cubic fourfolds. They both have crepant resolutions which are derived equivalent.


Complete Intersection Double Cover Exceptional Divisor Crepant Resolution Linear Subsystem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This paper is an extended exercise in Kuznetsov’s beautiful ideas about derived categories of cubic fourfolds [10], fractional Calabi–Yau categories [8, Section 4], and HPD [9]. Our debt to him is clear. We would like to warmly thank Nick Addington and Ed Segal for useful discussions. In addition, JC is grateful to Roland Abuaf, Michele Bolognesi, Enrica Floris, J\(\otimes \)rgen Rennemo and Brian Lehmann for helpful conversations on topics related to this paper. Finally, we would like to thank the referee for helpful comments. RT was partially supported by EPSRC programme Grant EP/G06170X/1 and JC was partially supported by NSF RTG Grant 1148609.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Rice University MS136HoustonUSA
  2. 2.Department of MathematicsImperial College LondonLondonUK

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