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arXiv · 1507.00682

The automorphism groups of Enriques surfaces covered by symmetric quartic surfaces

Shigeru Mukai·Hisanori Ohashi
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Abstract

Let $S$ be the (minimal) Enriques surface obtained from the symmetric quartic surface $(\sum_{i<j}x_ix_j)^2=kx_1x_2x_3x_4$ in $\mathbb{P}^3$ with $k\neq 0,4,36$, by taking quotient of the Cremona action $(x_i) \mapsto (1/x_i)$. The automorphism group of $S$ is a semi-direct product of a free product $\mathcal{F}$ of four involutions and the symmetric group $\mathfrak{S}_4$. Up to action of $\mathcal{F}$, there are exactly $29$ elliptic pencils on $S$.

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Shigeru Mukai, Hisanori Ohashi. 2015-07-02. The automorphism groups of Enriques surfaces covered by symmetric quartic surfaces. https://arxiv.org/abs/1507.00682

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