Abstract:

 Let M(k,n) be the moduli space of based (anti-self-dual) instantons on
\bar{CP^2} of charge k and rank n . There is a natural inclusion of rank n
instantons into rank n+1 . We show that the direct limit space is homotopy
equivalent to BU(k) x BU(k) . The moduli spaces also have the following
algebro-geometric interpretation: Let L be a line in the complex projective
plane and consider the blow-up at a point away from L.  M(k,n) can be
described as the moduli space of rank n holomorphic bundles on the blownup
projective plane with trivial 1st Chern clas, second Chern class equal to
k, and with a fixed holomorphic trivialization on L.