The Minimal Model Program and Resolution of cDV Singularity

Abstract

Our goal is to compute resolution of various types of singularities with a view towards the minimal model program. This thesis contains a general overview of the minimal model program together with practical techniques to deal with specific varieties and singularities. Thoroughly explained examples include the affine quadric cone, Del Pezzo surfaces, the cone over the Veronese surface, and Du Val singularities. At the end, we will observe a specific example of a resolution of a cDV singularity. Throughout the thesis, I also put emphasis on clearly stating techniques and results that are often taken for granted by people with working knowledge.