Calorons, Nahm's equations on S1 and bundles over P1 x P1

The moduli space of solutions to Nahm's equations of rank (k, k + j) on the circle, and hence, of SU(2) calorons of charge (k, j), is shown to be equivalent to the moduli of holomorphic rank 2 bundles on P-1 x P-1 trivialized at infinity ({infinity} x P-1 boolean OR P-1 x {infinity}) with c(2) = k and equipped with a flag of degree j along P-1 x {0}. An explicit matrix description of these spaces is given by a monad construction.