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On an Enriques Surface Associated With a Quartic Hessian Surface

  • Ichiro Shimada (a1)
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 $Y$ . 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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This work was supported by JSPS KAKENHI Grant Number 16H03926 and 16K13749.

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Canadian Journal of Mathematics
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