Deformation theory of Fuchsian equations and logarithmic connections

Details Deformation theory of Fuchsian equations and logarithmic connections Deformation theory of Fuchsian equations and logarithmic connections

2011-03-11

arxiv.org/abs/1103.2287v1

Mathematics

Differential Geometry

Rewritten material of the first part of arXiv:math/0703230. Submitted to Studia Scientiarum Mathematicarum Hungarica

Scientific paper

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.

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