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arXiv · 1701.00580

On an Enriques surface associated with a quartic Hessian surface

Ichiro Shimada
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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.

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Ichiro Shimada. 2017-01-03. On an Enriques surface associated with a quartic Hessian surface. https://doi.org/10.4153/cjm-2018-022-7

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