  This paper is devoted to algebro-geometric study of infinite dimensional Lie
bialgebras, which arise from solutions of the classical Yang-Baxter equation.
We regard trigonometric solutions of this equation as twists of the standard
Lie bialgebra cobracket on an appropriate affine Lie algebra and work out the
corresponding theory of Manin triples, putting it into an algebro-geometric
context. As a consequence of this approach, we prove that any trigonometric
solution of the classical Yang-Baxter equation arises from an appropriate
algebro-geometric datum. The developed theory is illustrated by some concrete
examples.

Algebraic Geometry;Quantum Algebra