Strange duality is shown to hold over generic K3 surfaces in a large number of cases. The isomorphism for elliptic K3 surfaces is established first via Fourier-Mukai techniques. Applications to Brill-Noether theory for sheaves on K3 surfaces are also obtained. The appendix, written by Kota Yoshioka, discusses the behavior of the moduli spaces under change of polarization, as needed in the argument.
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