Mathematische Annalen

, Volume 356, Issue 2, pp 439–467 | Cite as

Vector bundles on Fano varieties of genus ten

  • Michał Kapustka
  • Kristian Ranestad


In this note we describe a unique linear embedding of a prime Fano 4-fold \(F\) of genus 10 into the Grassmannian \(G(3,6)\). We use this to construct some moduli spaces of bundles on linear sections of \(F\). In particular the moduli space of bundles with Mukai vector \((3,L,3)\) on a generic polarized K3 surface \((S,L)\) of genus 10 is constructed as a double cover of \(\mathbf P ^2\) branched over a smooth sextic.

Mathematics Subject Classification (2000)

Primary 14D20 Secondary 14J45 14J28 



This work was completed while the first author visited University of Oslo between March 2009 and March 2010 supported by an EEA Scholarship and Training fund in Poland. We would like to thank G. Kapustka, J. Weyman, A. Kuznetsov, F. Han, S. Mukai, J. Buczyński, D. Anderson, and L. Manivel for discussions and remarks.


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Institute of MathematicsJagiellonian University of KrakówKrakówPoland
  2. 2.Department of MathematicsUniversity of OsloOsloNorway

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