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

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dc.creator García Prada, Oscar
dc.creator Hernández Ruipérez, Daniel
dc.creator Pioli, Fabio
dc.creator Tejero, Carlos
dc.date 2007-12-11T12:23:49Z
dc.date 2007-12-11T12:23:49Z
dc.date 2004-12-22
dc.date.accessioned 2017-01-31T00:59:27Z
dc.date.available 2017-01-31T00:59:27Z
dc.identifier arXiv:math/0406176v2
dc.identifier Journal of Geometry and Physics 55 (2005), no. 4, 353--384.
dc.identifier 0393-0440
dc.identifier http://hdl.handle.net/10261/2551
dc.identifier.uri http://dspace.mediu.edu.my:8181/xmlui/handle/10261/2551
dc.description 39 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.
dc.description 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.
dc.description The authors are members of VBAC (Vector bundles on algebraic curves), which is partially supported by EAGER (EC FP5 Contract no. HPRN-CT-2000-00099) and by EDGE (EC FP5 Contract no. HPRN-CT-2000-00101). This research has been partially supported by the Italian/Spain bilateral programme Azione Integrata, IT203 ”Sheaves on Calabi-Yau manifolds and applications to integrable systems and string theory” and by the research projects BFM2003-00097 of the Spanish DGI and SA118/03 of the “Junta de Castilla y León”.
dc.description Peer reviewed
dc.language eng
dc.publisher Elsevier
dc.relation Preprint
dc.rights openAccess
dc.subject Algebraic Geometry
dc.subject Differential Geometry
dc.title Fourier-Mukai and Nahm transforms for holomorphic triples on elliptic curves
dc.type Pre-print


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