Fourier–Mukai and Nahm transforms for holomorphic triples on elliptic curves
| Autor: | Carlos Tejero Prieto, Fabio Pioli, Daniel Hernández Ruipérez, Oscar García-Prada |
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| Rok vydání: | 2005 |
| Předmět: |
Mathematics - Differential Geometry
14J60 14H21 Fourier–Mukai transform Mathematical analysis Holomorphic function General Physics and Astronomy Vector bundle 14D20 14H60 Algebraic geometry Mathematics - Algebraic Geometry Elliptic curve symbols.namesake Fourier transform Differential Geometry (math.DG) Differential geometry Projective line FOS: Mathematics symbols Geometry and Topology Algebraic Geometry (math.AG) Mathematical Physics Mathematics |
| Zdroj: | Journal of Geometry and Physics. 55:353-384 |
| ISSN: | 0393-0440 |
| DOI: | 10.1016/j.geomphys.2004.12.013 |
| Popis: | 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. Comment: 39 pages, LaTeX2e, no figures; new proofs added, some arguments rewritten and typos corrected. Final version to appear in Journal of Geometry and Physics |
| Databáze: | OpenAIRE |
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