2000/06/30 by Marcos Jardim, Antony Maciocia
Mathematics · Physics and Astronomy · #math.AG #math-ph #math.MP
published as J. Reine Agnew. Math. 563 (2003) 221-235. · 17 pages. Final version to appear in Crelle
arxiv created 2002/12/16 · arxiv updated 2009/11/30
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.