FourierMukai transforms for K3 and elliptic fibrations
Authors:
Tom Bridgeland and Antony Maciocia
Journal:
J. Algebraic Geom. 11 (2002), 629657
DOI:
https://doi.org/10.1090/S105639110200317X
Published electronically:
March 18, 2002
MathSciNet review:
1910263
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Abstract  References  Additional Information
Abstract: Given a nonsingular variety with a K3 fibration $\pi \colon X\to S$ we construct dual fibrations $\hat {\pi }\colon Y\to S$ by replacing each fibre $X_s$ of $\pi$ 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 $\Phi \colon \operatorname {D}(Y)\to \operatorname {D}(X)$. 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.

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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
MR Author ID:
635821
ORCID:
000000015120006X
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
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