Given a non-singular variety with a K3 fibration pi: X --> S we construct dual fibrations pi: Y --> S by replacing each fibre X-s of pi by a two-dimensional moduli space of stable sheaves on X-s. In certain cases we prove that the resulting scheme Y is a non-singular variety and construct an equivalence of derived categories of coherent sheaves Phi: D(Y) --> D(X). Our methods also apply to elliptic and abelian surface fibrations. As an application we use the equivalences Phi to relate moduli spaces of stable bundles on elliptic threefolds to Hilbert schemes of curves.
|Number of pages||29|
|Journal||Journal of Algebraic Geometry|
|Publication status||Published - Oct 2002|