Complex ADHM equations and sheaves on

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