arXiv 1701.005802017-01math.AG

On an Enriques surface associated with a quartic Hessian surface

Ichiro Shimada

备注：: It turns out that Theorem 1.6 of the previous version contains a mistake. We replace Theorem 1.6 with a corrected statement
发表信息：: Can. J. Math.-J. Can. Math. 71 (2019) 213-246
DOI：: 10.4153/CJM-2018-022-7

英文摘要：

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.

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