Deformation theory of Fuchsian equations and logarithmic connections
  Motivated by a remark and a question of Nicholas Katz, we characterize the tangent space of the space of Fuchsian equations with given generic exponents inside the corresponding moduli space of logarithmic connections: we construct a weight 1 Hodge structure on the tangent space of the moduli of logarithmic connections such that deformations of Fuchsian equations correspond to the $(1,0)$-part. 
Szil\'ard Szab\'o
math.DG math.AG math.CA