We present a construction of framed torsion free instanton sheaves on a
projective variety containing a fixed line which further generalizes the one on
projective spaces. This is done by generalizing the so called ADHM variety. We
show that the moduli space of such objects is a quasi projective variety, which
is fine in the case of projective spaces. We also give an ADHM categorical
description of perverse instanton sheaves in the general case, along with a
hypercohomological characterization of these sheaves in the particular case of
projective spaces.Comment: 33 page
