In mathematics, the Springer resolution is a resolution

Resolution (algebra)

In mathematics, particularly in abstract algebra and homological algebra, a resolution is a sequence of objects which is used to describe the structure of a module, or, more generally, the structure of an object in an abelian category.Generally, if the objects involved in the sequence have a...

 of the variety of nilpotent

Nilpotent

In mathematics, an element x of a ring R is called nilpotent if there exists some positive integer n such that xn = 0....

 elements in a semisimple Lie algebra

Lie algebra

In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. Lie algebras were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" was introduced by Hermann Weyl in the...

, or the unipotent

Unipotent

In mathematics, a unipotent element r of a ring R is one such that r − 1 is a nilpotent element, in other words such that some power n is zero....

 elements of a reductive algebraic group, introduced by . The fibers of this resolution are called Springer fibers.

If U is the variety of unipotent elements in a reductive group

Reductive group

In mathematics, a reductive group is an algebraic group G over an algebraically closed field such that the unipotent radical of G is trivial . Any semisimple algebraic group is reductive, as is any algebraic torus and any general linear group...

 G, and X the variety of Borel subgroup

Borel subgroup

In the theory of algebraic groups, a Borel subgroup of an algebraic group G is a maximal Zariski closed and connected solvable algebraic subgroup.For example, in the group GLn ,...

s B, then the Springer resolution of U is the variety of pairs (u,B) of G×X such that u is in the Borel subgroup B. The map to U is the projection to the first factor.