Abstract
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.
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Acknowledgments
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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Kapustka, M., Ranestad, K. Vector bundles on Fano varieties of genus ten. Math. Ann. 356, 439–467 (2013). https://doi.org/10.1007/s00208-012-0856-3
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DOI: https://doi.org/10.1007/s00208-012-0856-3