In mathematics, the Springer resolution is a resolution of the variety of nilpotent elements in a semisimple Lie algebra,[1][2] or the unipotent elements of a reductive algebraic group, introduced by Tonny Albert Springer in 1969.
The Springer resolution for Lie algebras is similar, except that U is replaced by the nilpotent elements of the Lie algebra of G and X replaced by the variety of Borel subalgebras.
[5] The Grothendieck–Springer resolution is defined similarly, except that U is replaced by the whole group G (or the whole Lie algebra of G).
[6][7] When G=SL(2), the Lie algebra Springer resolution is T*P1 → n, where n are the nilpotent elements of sl(2).
n has a unique singular point 0, the fibre above which in the Springer resolution is the zero section P1 .