Instanton moduli as a novel map from tori to K3-surfaces

  title={Instanton moduli as a novel map from tori to K3-surfaces},
  author={Peter J. Braam and Antony Maciocia and Andrey N. Todorov},
  journal={Inventiones mathematicae},
A map is constructed from the moduli of hyper-Kähler tori to hyper-Kähler K3 surfaces which does not coincide with the Kummer map. The map takes a torus to the moduli space of SO(3) connections on a bundle with nontrivial first Stiefel-Whitney class and first Pontrjagin class equal to −4. This map is shown to intersect the Kummer moduli and also certain subvarieties of singular K3 surfaces. Our map is shown to satisfy the local Torelli theorem, and the K3-surfaces in its image are shown to… 
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