A Fourier-Mukai approach to spectral data for instantons

M Jardim, A Maciocia

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)221-235
Number of pages15
JournalJournal für die reine und angewandte Mathematik
Volume563
Publication statusPublished - Oct 2003

Keywords

  • ELLIPTIC FIBRATIONS
  • ABELIAN SURFACES
  • VECTOR-BUNDLES
  • NAHM TRANSFORM
  • STABLE SHEAVES
  • MONOPOLES

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