A note on resolution of rational and hypersurface singularities
Authors:
D. A. Stepanov
Affiliation:
Department of Mathematical Modeling, Bauman Moscow State Technical University, Moscow 105005, Russia
Abstract:
It is well known that the exceptional set in a resolution of a rational surface singularity is a tree of rational curves. We generalize the combinatoric part of this statement to higher dimensions and show that the highest cohomologies of the dual complex associated to a resolution of an isolated rational singularity vanish. We also prove that the dual complex associated to a resolution of an isolated hypersurface singularity is simply connected. As a consequence, we show that the dual complex associated to a resolution of a 3-dimensional Gorenstein terminal singularity has the homotopy type of a point.