2017/08/29 by Nigel Hitchin, Hitchin, Nigel
Mathematics · Physics and Astronomy · #14D21 #53C26 #53C28 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:14D21 #msc:53C26 #msc:53C28
paper · pdf · doi:10.48550/arxiv.1708.08812
To appear in a volume celebrating the work of Simon Donaldson
arxiv created 2017/08/29 · openalex publication_date 2017/08/29 · arxiv updated 2017/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Nahm's equations are viewed in a more general context where they appear as a vector field on a moduli space of co-Higgs bundles on the projective line. Zeros of this vector field correspond to torsion-free sheaves on a singular spectral curve which we translate in terms of a smooth curve in three-dimensional projective space. We also show how generalizations of Nahm's equations are required when the spectral curve is non-reduced and deduce the existence of non-classical conserved quantities in this situation.