This paper describes, in detail, a process for constructing Kummer K3 surfaces, and other "generalized" Kummer K3 surfaces. In particular, we look at how some well-known geometrical objects such as the platonic solids and regular polygons can inspire the creation of singular surfaces, and we investigate the resolution of those surfaces. Furthermore, we will extend this methodology to examine the singularities of some complex two-dimensional quotient spaces and resolve these singularities to construct a Kummer K3 and other generalized Kummer K3 surfaces.
Professor Justin Sawon, Department of Mathematics, University of North Carolina, Chapel Hill
"Simple Surface Singularities, their Resolutions, and Construction of K3 Surfaces,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 15
, Article 3.
Available at: https://scholar.rose-hulman.edu/rhumj/vol15/iss1/3