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

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dc.creatorGarcía-Prada, Oscar
dc.creatorRuipérez, Daniel Hernández
dc.creatorPioli, Fabio
dc.creatorPrieto, Carlos Tejero
dc.date2004-06-09
dc.date2004-12-22
dc.date.accessioned2026-07-07T06:18:07Z
dc.date.available2026-07-07T06:18:07Z
dc.descriptionWe 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.
dc.description39 pages, LaTeX2e, no figures; new proofs added, some arguments rewritten and typos corrected. Final version to appear in Journal of Geometry and Physics
dc.identifierhttps://arxiv.org/abs/math/0406176
dc.identifierhttp://arxiv.org/abs/math/0406176
dc.identifierJ. Geom. Phys. 55 (2005), no. 4, 353--384.
dc.identifierdoi:10.1016/j.geomphys.2004.12.013
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/94630
dc.subjectAlgebraic Geometry
dc.subjectDifferential Geometry
dc.subject14D20; 14H60; 14J60; 14H21
dc.titleFourier-Mukai and Nahm transforms for holomorphic triples on elliptic curves
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