  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.
