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}
}
  • Christian Böhning, H. G. Bothmer
  • 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
    • 8
    • PDF

    References

    SHOWING 1-10 OF 16 REFERENCES
    On the hypersurface of Luroth quartics
    • 21
    • PDF
    THE RATIONALITY OF MODULI SPACES OF HYPERELLIPTIC CURVES
    • 22
    Rationality of the moduli spaces of plane curves of sufficiently large degree
    • 5
    • PDF
    Lectures on Invariant Theory
    • 321
    • PDF
    Rationality of the moduli of hyperelliptic curves of arbitrary genus
    • 21
    Rationality of the fields of invariants
    • 32
    On the Luroth Quartic Curve
    • 21
    • Highly Influential
    On the birational geometry of (P)/GLn+1, Max-Planck
    • Institut Preprint,
    • 1994