English

A global analogue of the Springer resolution for $SL_2$

Algebraic Geometry 2013-01-07 v2 Representation Theory

Abstract

The global nilpotent cone N is a singular stack associated to the choice of an 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, and which is of emerging importance to the Classical Langlands Program. In analogy with the ordinary Springer resolution, we construct and study a resolution of singularities of N in the special case where G=SL_2. As an immediate application, we prove that N is equidimensional and also provide an enumeration of its irreducible components. We hope this is the first step in constructing a global Springer resolution for an arbitrary reductive group.

Keywords

Cite

@article{arxiv.1107.4826,
  title  = {A global analogue of the Springer resolution for $SL_2$},
  author = {Michael Skirvin},
  journal= {arXiv preprint arXiv:1107.4826},
  year   = {2013}
}

Comments

30 pages, several sections partially re-written, typos fixed, a few mathematical errors corrected