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

[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.

[发布日期] 2005-12-01

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