  Gaudin subalgebras are abelian Lie subalgebras of maximal dimension spanned
by generators of the Kohno-Drinfeld Lie algebra t_n. We show that Gaudin
subalgebras form a variety isomorphic to the moduli space of stable curves of
genus zero with n+1 marked points. In particular, this gives an embedding of
the moduli space in a Grassmannian of (n-1)-planes in an n(n-1)/2-dimensional
space. We show that the sheaf of Gaudin subalgebras over the moduli space 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 the
moduli space.
