A new construction of (D)over-tilde(5)-singularities and generalization of Slodowy slices

Any simple elliptic singularity of type (D) over tilde (5) can be obtained by taking the intersection of the nilpotent variety and the 4-dimensional "good slices" in the semi-simple Lie algebra sl(2, C) circle plus sl(2, C). We describe these new slices purely by the structure of the Lie algebra. We also construct the semi-universal deformation spaces of (D) over tilde (5)-singularities by using the 4-dimensional "good slices". (c) 2012 Elsevier Inc. All rights reserved.