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Lüroth quartic

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In mathematics, a Lüroth quartic is a nonsingular quartic plane curve containing the 10 vertices of a complete pentalateral. They were introduced by Jacob Lüroth (1869). Morley (1919) showed that the Lüroth quartics form an open subset of a degree 54 hypersurface, called the Lüroth hypersurface, in the space P14 of all quartics.

References

  • Lüroth, J. (1869), "Einige Eigenschaften einer gewissen Gattung von Curven vierter Ordnung", Mathematische Annalen, 1, Springer Berlin / Heidelberg: 37–53, doi:10.1007/BF01447385, ISSN 0025-5831, JFM 02.0511.02
  • Morley, Frank (1919), "On the Lüroth Quartic Curve", American Journal of Mathematics, 41 (4), The Johns Hopkins University Press: 279–282, ISSN 0002-9327
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