Deformations of Fuchsian Equations
نویسنده
چکیده
— We prove that the dimension of the deformations of a given generic Fuchsian system without changing the conjugacy class of its local monodromies (“number of accessory parameters”) is equal to half the dimension of the moduli space of deformations of the associated local system. We do this by constructing a weight 1 Hodge structure on the infinitesimal deformations of integrable connections. We then show that the tangent of the Hitchin map restricted to the tangent space of deformations of the Fuchsian system is an isomorphism.
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ar X iv : m at h / 07 03 23 0 v 3 [ m at h . A G ] 1 6 Ja n 20 08 DEFORMATIONS OF FUCHSIAN EQUATIONS AND LOGARITHMIC CONNECTIONS
— We give a geometric proof to the classical fact that the dimension of the deformations of a given generic Fuchsian equation without changing the semi-simple conjugacy class of its local monodromies (“number of accessory parameters”) is equal to half the dimension of the moduli space of deformations of the associated local system. We do this by constructing a weight 1 Hodge structure on the in...
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