English

On an Enriques surface associated with a quartic Hessian surface

Algebraic Geometry 2020-09-01 v7

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.

Keywords

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

R2 v1 2026-06-22T17:39:41.932Z