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.