On Enriques surfaces with four cusps

Abstract

We study Enriques surfaces with four A_2-configurations. In particular, we construct open Enriques surfaces with fundamental groups (Z/3Z)^2 x Z/2Z and Z/6Z, completing the picture of the A_2-case from previous work by Keum and Zhang. We also construct an explicit Gorenstein Q-homology projective plane of singularity type A3 + 3A2, supporting an open case from a paper by Hwang, Keum and Ohashi.

29 pages, 1 figure; v3: Lemma 2.1 added, proof of Lemma 2.3 reorganized and streamlined

References in corpus (3)

• Gorenstein $\mathbb{Q}$-homology projective planes
• Elliptic K3 surfaces with geometric Mordell-Weil rank 15
• Moduli of Gorenstein Q-homology projective planes

Cited by in corpus (3)

• When are Zariski chambers numerically determined?
• Rational double points on Enriques surfaces
• Singularities of normal quartic surfaces III (char=2, non-supersingular)