2002/05/23 by Tamas Hausel, Tam�s Hausel, Michael Thaddeus · 7 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #Computation #Computer science #Dual (grammatical number) #Duality (order theory) #Geometry #Langlands dual group #Langlands program #Linguistics #Mathematics #Mirror symmetry #Pure mathematics #Space (punctuation) #Symmetry (geometry) #hep-th #math-ph #math.AG #math.DG #math.MP #msc:14D21 #msc:14H40 #msc:14H60 #msc:14H70 #msc:32S35
paper · pdf · doi:10.1007/s00222-003-0286-7
31 pages, LaTeX with packages amsfonts, latexsym, [dvips]graphicx, [dvips]color, one embedded postscript figure
arxiv created 2002/05/23 · openalex publication_date 2003/07/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the moduli spaces of flat SL(r)- and PGL(r)-connections, or equivalently, Higgs bundles, on an algebraic curve. These spaces are noncompact Calabi-Yau orbifolds; we show that they can be regarded as mirror partners in two different senses. First, they satisfy the requirements laid down by Strominger-Yau-Zaslow (SYZ), in a suitably general sense involving a B-field or flat unitary gerbe. To show this, we use their hyperkahler structures and Hitchin's integrable systems. Second, their Hodge numbers, again in a suitably general sense, are equal. These spaces provide significant evidence in support of SYZ. Moreover, they throw a bridge from mirror symmetry to the duality theory of Lie groups and, more broadly, to the geometric Langlands program.