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A Fourier-Mukai approach to spectral data for instantons

Marcos Jardim·Antony Maciocia
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Abstract

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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Marcos Jardim, Antony Maciocia. 2002-12-16. A Fourier-Mukai approach to spectral data for instantons. https://arxiv.org/abs/math/0006054

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