Spectral curves and Nahm transform for doubly-periodic instantons

Details Spectral curves and Nahm transform for doubly-periodic instantons Spectral curves and Nahm transform for doubly-periodic instantons

1999-09-24

arxiv.org/abs/math/9909146v2

Commun. Math. Phys. 225 (2002), 639-668 (combined with math.DG/9910120).

Mathematics

Algebraic Geometry

Completely reformulated, more differential-geometric approach. 12 pages

Scientific paper

10.1007/s002200100596

We explore the role played by the spectral curves associated with Higgs pairs in the context of the Nahm transform of doubly-periodic instantons defined in "Construction of doubly-periodic instantons" (math.DG/9909069) and "Nahm transform for doubly-periodic instantons" (math.DG/9910120). More precisely, we show how to construct a triple consisting of an algebraic curve plus a line bundle with connection over it from a doubly-periodic instanton, and that these coincide with the Hitchin's spectral data associated with the Nahm transformed Higgs bundle.

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