Fourier-Mukai transforms for K3 and elliptic fibrations

Abstract

Given a non-singular variety with a K3 fibration f : X --> S we construct dual fibrations Y --> S by replacing each fibre X_s of f 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 Φ: D(Y) --> D(X). Our methods also apply to elliptic and abelian surface fibrations. As an application we show how the equivalences Φidentify certain moduli spaces of stable bundles on elliptic threefolds with Hilbert schemes of curves.

This version corrects a couple of errors; see footnotes on pages 9 and 16

References in corpus (2)

• Frobenius Manifolds and Formality of Lie Algebras of Polyvector Fields
• Mukai implies McKay: the McKay correspondence as an equivalence of derived categories

Cited by in corpus (5)

• Mukai implies McKay: the McKay correspondence as an equivalence of derived categories
• Fourier-Mukai Transform and Mirror Symmetry for D-Branes on Elliptic Calabi-Yau
• Bridgeland Stability conditions on threefolds I: Bogomolov-Gieseker type inequalities
• Standard-model bundles
• Brill-Noether theory for curves on generic abelian surfaces