= Solution
The reverse-oriented <Complex projective plane> has <intersection form> $(-1)$, so $b^+=0$, while $b_1=0$. The <Hodge star> splits harmonic two-forms into self-dual and anti-self-dual subspaces, and their dimensions are the positive and negative indices of the <intersection form>. Therefore every harmonic two-form is an <anti-self-dual two-form> for every chosen metric.
By part (b), every <complex line bundle> has a <unitary connection> with harmonic real <vector-bundle curvature>, so this connection is an <ASD connection>. Conversely, an <ASD connection> on a <complex line bundle> has $dF=0$ and $d*F=-dF=0$, so its <vector-bundle curvature> is harmonic. The uniqueness in part (b) therefore applies to all <ASD connections> on that fixed <complex line bundle>. \b[Each <complex line bundle> has exactly one gauge orbit of ASD connections.]
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