FourierMukai transforms for K3 and elliptic fibrations
Abstract
Given a nonsingular variety with a K3 fibration f : X > S we construct dual fibrations Y > S by replacing each fibre X_s of f by a twodimensional moduli space of stable sheaves on X_s. In certain cases we prove that the resulting scheme Y is a nonsingular 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 show how the equivalences \Phi identify certain moduli spaces of stable bundles on elliptic threefolds with Hilbert schemes of curves.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 August 1999
 arXiv:
 arXiv:math/9908022
 Bibcode:
 1999math......8022B
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 This version corrects a couple of errors