Moduli spaces of framed instanton sheaves on pojective spaces

We introduce a generalization of Atiyah-Drinfeld-Hitchin-Manin linear algebraic data and a generalization of Atiyah-Drinfeld-Hitchin-Manin equation, which are subsequently used to construct all framed instanton bundles on complex projective spaces. Using geometric invariant theory, we prove that the moduli spaces of framed instanton sheaves is a quiasiprojective variety. We also provided a link between the generalized ADHM data introduced here and certain representaions of quivers.