Obstructions and hypersurface sections (minimally elliptic singularities)

Abstract

We study the obstruction space T 2 {T^2} for minimally elliptic surface singularities. We apply the main lemma of our previous paper [3] which relates T 2 {T^2} to deformations of hypersurface sections. To use this we classify general hypersurface sections of minimally elliptic singularities. As in the rational singularity case there is a simple formula for the minimal number of generators for T 2 {T^2} as a module over the local ring. This number is in many cases (e.g. for cusps of Hilbert modular surfaces) equal to the vector space dimension of T 2 {T^2} .