Volume 280, Number 2, 315-349, DOI: 10.1007/s00220-008-0468-7

Calorons, Nahm’s Equations on S 1 and Bundles over \mathbbP1 ×\mathbbP1{\mathbb{P}^{1} \times \mathbb{P}^{1}}

Benoit Charbonneau and Jacques Hurtubise

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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 \mathbbP1 ×\mathbbP1{\mathbb{P}^{1} \times \mathbb{P}^{1}} trivialized at infinity ( {¥} ×\mathbbP1 È\mathbbP1 ×{¥}{\{\infty\} \times \mathbb{P}^{1} \cup \mathbb{P}^{1} \times \{\infty\}}) with c 2 = k and equipped with a flag of degree j along \mathbbP1 ×{0}{\mathbb{P}^1 \times \{0\}}. An explicit matrix description of these spaces is given by a monad construction.
Communicated by G.W. Gibbons

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