Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fourier-Mukai transforms for K3 and elliptic fibrations   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 \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.

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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg