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

Notes

Acknowledgments

Both authors were supported by the German Research Foundation [Deutsche Forschungsgemeinschaft (DFG)] through the Institutional Strategy of the University of Göttingen.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2011

Authors and Affiliations

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

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