ON CONJUGACY CLASSES OF THE KLEIN SIMPLE GROUP IN CREMONA GROUP

ON CONJUGACY CLASSES OF THE KLEIN SIMPLE GROUP IN CREMONA GROUP

We consider countably many three-dimensional PSL2( $\mathbb{F}$ 7)-del Pezzo surface fibrations over ℙ1. Conjecturally, they are all irrational except two families, one of which is the product of a del Pezzo surface with ℙ1. We show that the other model is PSL2( $\mathbb{F}$ 7)-equivariantly biratio...

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Veröffentlicht in:Glasgow mathematical journal 2017-05, Vol.59 (2), p.395-400
1. Verfasser: AHMADINEZHAD, HAMID
Format: Artikel
Sprache:eng
Schlagworte:
Geometry
Mathematical models
Subgroups
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Zusammenfassung:We consider countably many three-dimensional PSL2( $\mathbb{F}$ 7)-del Pezzo surface fibrations over ℙ1. Conjecturally, they are all irrational except two families, one of which is the product of a del Pezzo surface with ℙ1. We show that the other model is PSL2( $\mathbb{F}$ 7)-equivariantly birational to ℙ2×ℙ1. Based on a result of Prokhorov, we show that they are non-conjugate as subgroups of the Cremona group Cr3(ℂ).
ISSN:0017-0895
1469-509X
DOI:10.1017/S0017089516000239