Lüroth quartic
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. Böhning & von Bothmer (2011) proved that the moduli space of Lüroth quartics is rational.
References
- Böhning, Christian; von Bothmer, Hans-Christian (2011), "On the rationality of the moduli space of Lüroth quartics", Mathematische Annalen, Springer Berlin / Heidelberg: 1–9, ISSN 0025-5831, doi:10.1007/s00208-011-0715-7
- Lüroth, J. (1869), "Einige Eigenschaften einer gewissen Gattung von Curven vierter Ordnung", Mathematische Annalen, Springer Berlin / Heidelberg, 1: 37–53, ISSN 0025-5831, JFM 02.0511.02, doi:10.1007/BF01447385
- Morley, Frank (1919), "On the Lüroth Quartic Curve", American Journal of Mathematics, The Johns Hopkins University Press, 41 (4): 279–282, ISSN 0002-9327, JSTOR 2370287, doi:10.2307/2370287
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