Generic strange duality for $K3$ surfaces

摘要

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