In mathematics, a Lüroth quartic is a nonsingular quartic

plane curve In mathematics, a plane curve is a curve in a plane that may be either a Euclidean plane, an affine plane or a projective plane. The most frequently studied cases are smooth plane curves (including piecewise smooth plane curves), and algebraic ...

containing the 10 vertices of a complete pentalateral. They were introduced by . showed that the Lüroth quartics form an open subset of a degree 54

hypersurface In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface. A hypersurface is a manifold or an algebraic variety of dimension , which is embedded in an ambient space of dimension , generally a Euclidea ...

, called the Lüroth hypersurface, in the space P¹⁴ of all quartics. proved that the moduli space of Lüroth quartics is rational.

References

* * * {{DEFAULTSORT:Luroth Quartic Algebraic curves