Sheaf lines of Yang–Mills instanton sheaves

Abstract

We calculate a sheaf line in [Formula: see text] which is the real line supporting sheaf points on [Formula: see text] of [Formula: see text] Yang–Mills (YM) instanton (or [Formula: see text] complex YM instanton) sheaves for some given ADHM data we obtained previously. We found that this sheaf line is indeed a special jumping line over [Formula: see text] spacetime. In addition, we calculate the singularity structure of the connection [Formula: see text] and the field strength [Formula: see text] at the corresponding singular point on [Formula: see text] of this sheaf line. We found that the order of singularity at the singular point on [Formula: see text] associated with the sheaf line in [Formula: see text] is higher than those of other singular points associated with normal jumping lines. We conjecture that this is a general feature for sheaf lines among jumping lines.