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

AutorGarcía Prada, Oscar; Hernández Ruipérez, Daniel; Pioli, Fabio; Tejero, Carlos
Palabras claveAlgebraic Geometry
Differential Geometry
Fecha de publicación22-dic-2004
EditorElsevier
CitaciónarXiv:math/0406176v2
Journal of Geometry and Physics 55 (2005), no. 4, 353--384.
ResumenWe 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.
Descripción39 pages, LaTeX2e, no figures; new proofs added in Version nr. 2, some arguments rewritten and typos corrected. Final version to appear in Journal of Geometry and Physics.
URIhttp://hdl.handle.net/10261/2551
ISSN0393-0440
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