Instanton moduli as a novel map from tori to K3-surfaces |
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| Authors: | Peter J Braam Antony Maciocia Andrey Todorov |
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| Institution: | (1) The Mathematical Institute, Oxford University, 24-29 St. Giles, 3LB Oxford, OX, UK;(2) Department of Mathematics, Edinburgh University, Mayfield Road, EH9 3JZ Edinburgh, UK;(3) Department of Mathematics, University of California, Santa Cruz, USA |
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| Abstract: | 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 carry a natural metric which is Calabi-Yau. |
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