, Volume 353, Issue 4, pp 1273-1281,
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On the rationality of the moduli space of Lüroth quartics

Abstract

We prove that the moduli space \({\mathfrak{M}_L}\) of Lüroth quartics in \({\mathbb{P}^2}\) , i.e. the space of quartics which can be circumscribed around a complete pentagon of lines modulo the action of \({\mathrm{PGL}_3 (\mathbb{C})}\) is rational, as is the related moduli space of Bateman seven-tuples of points in \({\mathbb{P}^2}\) .