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Autoequivalences of Derived Category of A K3 Surface and Monodromy Transformations

Shinobu Hosono University of Tokyo Bong H. Lian Brandeis University Keiji Oguiso University of Tokyo Shing-Tung Yau Harvard University

mathscidoc:1608.01027

Journal of Algebraic Geometry, 13, 513-545 , 2004
We consider autoequivalences of the bounded derived category of coherent sheaves on a K3 surface. We prove that the image of the autoequivalences has index at most two in the group of the Hodge isometries of the Mukai lattice. Motivated by homological mirror symmetry we also consider the mirror counterpart, i.e. symplectic version of it. In the case of $\rho (X)=1 $, we find an explicit formula which reproduces the number of Fourier-Mukai (FM) partners from the monodromy problem of the mirror K3 family. We present an explicit example in which a monodromy action does not come from an autoequivalence of the mirror side.
K3 Surface, Monodromy Transformations, Hodge isometries, Mukai lattice
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@inproceedings{shinobu2004autoequivalences,
  title={Autoequivalences of Derived Category of A K3 Surface and Monodromy Transformations},
  author={Shinobu Hosono, Bong H. Lian, Keiji Oguiso, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160828165855029954492},
  booktitle={Journal of Algebraic Geometry},
  volume={13},
  pages={513-545 },
  year={2004},
}
Shinobu Hosono, Bong H. Lian, Keiji Oguiso, and Shing-Tung Yau. Autoequivalences of Derived Category of A K3 Surface and Monodromy Transformations. 2004. Vol. 13. In Journal of Algebraic Geometry. pp.513-545 . http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160828165855029954492.
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