Deformation And Resolution Of Surface Singularities

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/ð€€€, where ð€€€ 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.