2026/03/23 by Nigel Hitchin · 1 citation
Mathematics · Physics and Astronomy · #Homotopy and Cohomology in Algebraic Topology #Black Holes and Theoretical Physics #Algebraic Geometry and Number Theory
paper · pdf · doi:10.1016/j.geomphys.2026.105955
The article gives a differential geometric construction of the complex structure on the total space of the family of moduli spaces of Higgs bundles on a curve C , as a fibration over Teichmüller space. The method uses a real valued function f defined on the character variety, essentially the energy of a harmonic map, which is dependent on the complex structure of C . Using f we define a natural Ehresmann connection with structure group the Hamiltonian diffeomorphisms of the fibre and using the associated horizontal distribution define an almost complex structure which we show to be integrable. The formalism parallels the usual variation of Hodge structure in this nonabelian version.