Fourier-Mukai transforms for K3 and elliptic fibrations

Authors:
Tom Bridgeland and Antony Maciocia

Journal:
J. Algebraic Geom. **11** (2002), 629-657

Published electronically:
March 18, 2002

MathSciNet review:
1910263

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Abstract | References | Additional Information

Abstract: Given a non-singular variety with a K3 fibration we construct dual fibrations by replacing each fibre of by a two-dimensional moduli space of stable sheaves on . In certain cases we prove that the resulting scheme is a non-singular variety and construct an equivalence of derived categories of coherent sheaves . Our methods also apply to elliptic and abelian surface fibrations. As an application we use the equivalences to relate moduli spaces of stable bundles on elliptic threefolds to Hilbert schemes of curves.

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Additional Information

**Tom Bridgeland**

Affiliation:
Department of Mathematics and Statistics, The University of Edinburgh, King’s Buildings, Mayfield Road, Edinburgh, EH9 3JZ, United Kingdom

Email:
tab@maths.ed.ac.uk

**Antony Maciocia**

Affiliation:
Department of Mathematics and Statistics, The University of Edinburgh, King’s Buildings, Mayfield Road, Edinburgh, EH9 3JZ, United Kingdom

Email:
A.Maciocia@ed.ac.uk

DOI:
https://doi.org/10.1090/S1056-3911-02-00317-X

Received by editor(s):
May 23, 2000

Published electronically:
March 18, 2002

Additional Notes:
This research was carried out with the support of the Engineering and Physical Sciences Research Council of Great Britain