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The global nilpotent cone N is a singular stack associated to the choice ofan algebraic group G, a smooth projective curve X, and a line bundle L on X,which is of fundamental importance to the Geometric Langlands Program, andwhich is of emerging importance to the Classical Langlands Program. In analogywith the ordinary Springer resolution, we construct and study a resolution ofsingularities of N in the special case where G=SL_2. As an immediateapplication, we prove that N is equidimensional and also provide an enumerationof its irreducible components. We hope this is the first step in constructing aglobal Springer resolution for an arbitrary reductive group.

A global analogue of the Springer resolution for $SL_2$