A Fourier transform for Higgs bundles

Details A Fourier transform for Higgs bundles A Fourier transform for Higgs bundles

2001-04-26

arxiv.org/abs/math/0104253v1

Mathematics

Algebraic Geometry

20 pages

Scientific paper

We define a Fourier-Mukai transform for Higgs bundles on smooth curves and study its properties. It is shown that the transform of a stable zero-degree Higgs bundle is an algebraic vector bundle on the cotangent bundle of the Jacobian of the curve. We show that this transformed bundle admits a natural extension to an algebraic vector bundle over a projective compactification of the base. The main result is that the original Higgs bundle can be reconstructed from this extension. We also compute certain invariants of the transformed bundle.

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