Abstract
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 \({\mathbb{P}^{1} \times \mathbb{P}^{1}}\) trivialized at infinity (\({\{\infty\} \times \mathbb{P}^{1} \cup \mathbb{P}^{1} \times \{\infty\}}\)) with c 2 = k and equipped with a flag of degree j along \({\mathbb{P}^1 \times \{0\}}\). An explicit matrix description of these spaces is given by a monad construction.
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Communicated by G.W. Gibbons
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Charbonneau, B., Hurtubise, J. Calorons, Nahm’s Equations on S 1 and Bundles over \({\mathbb{P}^{1} \times \mathbb{P}^{1}}\) . Commun. Math. Phys. 280, 315–349 (2008). https://doi.org/10.1007/s00220-008-0468-7
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DOI: https://doi.org/10.1007/s00220-008-0468-7