Strange duality is shown to hold over generic surfaces in a large number of cases. The isomorphism for elliptic surfaces is established first via Fourier–Mukai techniques. Applications to Brill–Noether theory for sheaves on 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.
"Generic strange duality for surfaces." Duke Math. J. 162 (8) 1463 - 1501, 1 June 2013. https://doi.org/10.1215/00127094-2208643