We study SU(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 surface, we show that the moduli space of instantons has a natural Lagrangian fibration structure with respect to the canonical complex symplectic structures.
|Number of pages||15|
|Journal||Journal für die reine und angewandte Mathematik|
|Publication status||Published - Oct 2003|
- ELLIPTIC FIBRATIONS
- ABELIAN SURFACES
- NAHM TRANSFORM
- STABLE SHEAVES