Abstract
In this dissertation, we study ADE surface singularities in terms of Dynkin diagram
obtained by deforming and resolving the singularity. Using classic invariant theory,
we describe how these surface emerge as quotient of C2/, where SL2(C), is
a finite subgroup of the group of 2×2 matrix of determinant 1 over C. We further
describe how these hypersurface embed in C3 as an affine varieties. We deform An
type singularity and show its relation to McKay-quivers.
Finally, we investigate the the exceptional locus of the resolution of the those isolated
singularities using sequence of blowup and from this we obtain the corresponding
Dynkin diagram of ADE type.