# On the rationality of the moduli space of Lüroth quartics

@article{Bhning2010OnTR,
title={On the rationality of the moduli space of L{\"u}roth quartics},
author={Christian B{\"o}hning and H. G. Bothmer},
journal={Mathematische Annalen},
year={2010},
volume={353},
pages={1273-1281}
}
• Published 2010
• Mathematics
• Mathematische Annalen
• 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 $${\mathbb{P}^2}$$.
1 Citations
An explicit expression of the Lüroth invariant
• Mathematics, Computer Science
• ISSAC '13
• 2013
• 8
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