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arXiv · 1310.5548

On conjugacy classes of the Klein simple group in Cremona group

Hamid Abban
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Abstract

We consider countably many three dimensional $\mathtt{PSL}_2(\mathbb{F}_7)$-del Pezzo surface fibrations over $\mathbb{P}^1$. Conjecturally they are all irrational except two families, one of which is the product of a del Pezzo surface with $\mathbb{P}^1$. We show that the other model is $\mathtt{PSL}_2(\mathbb{F}_7)$-equivariantly birational to $\mathbb{P}^2\times\mathbb{P}^1$. Based on a result of Prokhorov, we show that they are non-conjugate as subgroups of the Cremona group $\mathtt{Cr}_3(\mathbb{C})$.

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Hamid Abban. 2013-10-21. On conjugacy classes of the Klein simple group in Cremona group. https://arxiv.org/abs/1310.5548

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