Mathematische Annalen

, Volume 353, Issue 4, pp 1273–1281 | Cite as

On the rationality of the moduli space of Lüroth quartics

  • Christian Böhning
  • Hans-Christian Graf von Bothmer
Open Access


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 \({\mathbb{P}^2}\).


Modulus Space Hyperelliptic Curve Mathematical Society Lecture Note Series Plane Quartic Branch Curve 
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Both authors were supported by the German Research Foundation [Deutsche Forschungsgemeinschaft (DFG)] through the Institutional Strategy of the University of Göttingen.

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© The Author(s) 2011

Authors and Affiliations

  • Christian Böhning
    • 1
  • Hans-Christian Graf von Bothmer
    • 1
  1. 1.GöttingenGermany

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