Gaudin subalgebras and stable rational curves
2014-07-16T15:53:59Z (GMT) by
Gaudin subalgebras are abelian Lie subalgebras of maximal dimension spanned by generators of the Kohno-Drinfeld Lie algebra tn. We show that Gaudin subalgebras form a variety isomorphic to the moduli space M 0;n+1 of stable curves of genus zero with n+1 marked points. In particular, this gives an embedding of M 0;n+1 in a Grassmannian of (n-1)-planes in an n(n-1)=2-dimensional space. We show that the sheaf of Gaudin subalgebras over M 0;n+1 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 M 0;n+1.