A Fourier-Mukai approach to spectral data for instantons

Details A Fourier-Mukai approach to spectral data for instantons A Fourier-Mukai approach to spectral data for instantons

2000-06-07

arxiv.org/abs/math/0006054v2

J. Reine Agnew. Math. 563 (2003) 221-235.

Mathematics

Algebraic Geometry

17 pages. Final version to appear in Crelle

Scientific paper

We study U(r) instantons on elliptic surfaces with a section and show that they are in one-one correspondence with spectral data consisting of a curve in the dual elliptic surface and a line bundle on that curve. We use relative Fourier-Mukai transforms to analyse their properties and, in the case of the K3 and abelian surfaces, we show that the moduli space of instantons has a natural Lagrangian fibration with respect to the canonical complex symplectic structure.

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