Vector bundles on Fano threefolds and K3 surfaces

  title={Vector bundles on Fano threefolds and K3 surfaces},
  author={Arnaud Beauville},
  journal={arXiv: Algebraic Geometry},
  • A. Beauville
  • Published 2019
  • Mathematics
  • arXiv: Algebraic Geometry
Let X be a Fano threefold, and let S be a K3 surface in X . Any moduli space M of simple vector bundles on S carries a holomorphic symplectic structure. Following an idea of Tyurin, we show that in some cases, those vector bundles which come from X form a Lagrangian subvariety of M . We illustrate this with a number of concrete examples. 
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