On an Enriques surface associated with a quartic Hessian surface
Abstract
Let Y be a complex Enriques surface whose universal cover X is birational to a general quartic Hessian surface. Using the result on the automorphism group of X due to Dolgachev and Keum, we obtain a finite presentation of the automorphism group of Y. A fundamental domain of the action of the automorphism group on the nef cone of Y is described explicitly. The list of elliptic fibrations on Y and the list of combinations of rational double points that can appear on a surface birational to Y are presented. As an application, a set of generators of the automorphism group of the generic Enriques surface is calculated explicitly.
Cite
@article{arxiv.1701.00580,
title = {On an Enriques surface associated with a quartic Hessian surface},
author = {Ichiro Shimada},
journal= {arXiv preprint arXiv:1701.00580},
year = {2020}
}
Comments
It turns out that Theorem 1.6 of the previous version contains a mistake. We replace Theorem 1.6 with a corrected statement