Gorenstein $\mathbb{Q}$-homology projective planes

Abstract

We present the complete list of all singularity types on Gorenstein $\mathbb{Q}$-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.

Added in Proof. The type $A_3\oplus 3A_2$ realizes on the Enriques surface constructed by Slawomir Rams and Matthias Schütt [On Enriques surfaces with four cusps, arXiv:1404.3924, Example 3.9]

Cited by in corpus (5)

• On Enriques surfaces with four cusps
• Moduli of Gorenstein Q-homology projective planes
• Rational double points on Enriques surfaces
• Q_l-cohomology projective planes from Enriques surfaces in odd characteristic
• On lens spaces bounding smooth 4-manifolds with ${\mathbf{b}}_2=1$