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

JOURNAL OF GEOMETRY AND PHYSICS

卷:55

Article

García-Prada, O ; Ruipérez, DH ; Pioli, F ; Prieto, CT

关键词: Fourier-Mukai transform;    stable triples;    elliptic curves;    Nahm transform;    holomorphic triples;   

DOI  :  10.1016/j.geomphys.2004.12.013

来源: Elsevier

【 摘 要 】

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. (c) 2004 Elsevier B.V. All rights reserved.

【 授权许可】

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