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Fourier-Mukai and Nahm transforms for holomorphic triples on elliptic curves

Oscar García-Prada·Daniel Hernández Ruipérez·Fabio Pioli·Carlos Tejero Prieto
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Abstract

We define a Fourier-Mukai transform for a triple consisting of two holomorphic vector bundles over an elliptic curve and a homomorphism between them. We prove that in some cases the transform preserves the natural stability condition for a triple. We also define a Nahm transform for solutions to natural gauge-theoretic equations on a triple -- vortices -- and explore some of its basic properties. Our approach combines direct methods with dimensional reduction techniques, relating triples over a curve with vector bundles over the product of the curve with the complex projective line.

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Oscar García-Prada, Daniel Hernández Ruipérez, Fabio Pioli, Carlos Tejero Prieto. 2004-12-22. Fourier-Mukai and Nahm transforms for holomorphic triples on elliptic curves. https://doi.org/10.1016/j.geomphys.2004.12.013

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