We establish a 1-1 correspondence between certain classes of sheaves on P-3 and solutions of a complex version of the Atiyah-Hitchin-Drinfeld-Manin equations. We also show how relaxing of the locally free condition on sheaves is reflected on partial completions of the space of regular solutions. We also introduce a new class of sheaves on P-3 closely related to ideal sheaves for curves within P3. (C) 2008 Elsevier Inc. All rights reserved.319729132937