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Gaudin subalgebras are abelian Lie subalgebras of maximal dimension spanned by generators of the Kohno-Drinfeld Lie algebra \Xmathfrak {t}_{\hspace *{.3pt}n}. We show that Gaudin subalgebras form a variety isomorphic to the moduli space MΛ0,n+1β of stable curves of genus zero with n+1 marked points. In particular, this gives an embedding of MΛ0,n+1β in a Grassmannian of (nβ1)-planes in an n(nβ1)/2-dimensional space. We show that the sheaf of Gaudin subalgebras over MΛ0,n+1β is isomorphic to a sheaf of twisted first-order differential operators. For each representation of the Kohno-Drinfeld Lie algebra with fixed central character, we obtain a sheaf of commutative algebras whose spectrum is a coisotropic subscheme of a twisted version of the logarithmic cotangent bundle of $\bar M_{0,n+1}
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