2 00 7 Deformations of Fuchsian Equations and Systems
نویسنده
چکیده
— We explain why the dimension of the deformations of a given generic Fuchsian equation 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, such that deformations as an equation correspond to the (1, 0)-part. This answers a question of Nicholas Katz, who noticed the dimension doubling mentioned above. We then show that the tangent of the Hitchin map restricted to the tangent space of deformations of the Fuchsian equation is an isomorphism.
منابع مشابه
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