Complex ADHM equations and sheaves on P3

We establish a 1-1 correspondence between certain classes of sheaves on P3 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 P3 closely related to ideal sheaves for curves within P3.