DongSeon Hwang

Construction of singular rational surfaces of Picard number one with ample canonical divisor

Kollar gave a series of examples of rational surfaces of Picard number 1 with ample canonical divisor having cyclic singularities. In this paper, we construct several series of new examples in a geometric way, i.e., by blowing up several times inside a configuration of curves on the projective plane and then by contracting chains of rational curves. One series of our examples have the same singularities as Kollar’s examples.

Gorenstein ℚ-homology projective planes

We present the complete list of all singularity types on Gorenstein ℚ-homology projective planes, i.e., normal projective surfaces of second Betti number one with at worst rational double points. The list consists of 58 possible singularity types, each except two types supported by an example.