Details

Autor(en) / Beteiligte

• García-Prada, Oscar
• Hernández Ruipérez, Daniel
• Pioli, Fabio
• Tejero Prieto, Carlos

Titel

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

Ist Teil von

• Journal of geometry and physics, 2005-12, Vol.55 (4), p.353-384

Ort / Verlag

Elsevier B.V

Erscheinungsjahr

2005

Link zum Volltext

Quelle

Elsevier ScienceDirect Journals Complete

Beschreibungen/Notizen

• 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.