Lüroth quartic

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title: "Lüroth quartic" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["quartic-curves"] topic_path: "general/quartic-curves" source: "https://en.wikipedia.org/wiki/Lüroth_quartic" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

::figure[src="https://upload.wikimedia.org/wikipedia/commons/5/55/Luroth_quartic.svg" caption="Some examples of '''Lüroth quartics'''"] ::

In mathematics, a Lüroth quartic is a nonsingular quartic plane curve 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, called the Lüroth hypersurface, in the space P14 of all quartics. proved that the moduli space of Lüroth quartics is rational.

References

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