Asymptotic behaviour and the moduli space of doublyperiodic instantons
Abstract
We study doublyperiodic instantons, i.e. instantons on the product of a 1dimensional complex torus T with a complex line C, with quadratic curvature decay. We determine the asymptotic behaviour of these instantons, constructing new asymptotic invariants. We show that the underlying holomorphic bundle extends to TxP1. The converse statement is also true, namely a holomorphic bundle on TxP1 which is flat on the torus at infinity, and satisfies a stability condition, comes from a doublyperiodic instanton. Finally, we study the hyperkahler geometry of the moduli space of doublyperiodic instantons, and prove that the Nahm transform previously defined by the second author is a hyperkahler isometry with the moduli space of certain meromorphic Higgs bundles on the dual torus.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2000
 arXiv:
 arXiv:math/0005154
 Bibcode:
 2000math......5154B
 Keywords:

 Differential Geometry;
 Mathematical Physics