Gaudin subalgebras and stable rational curves
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 em...
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Main Authors: | , , |
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Format: | Default Article |
Published: |
2011
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Subjects: | |
Online Access: | https://hdl.handle.net/2134/15216 |
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Summary: | 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. |
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