Quartic threefold

In algebraic geometry, a quartic threefold is a degree 4 hypersurface of dimension 3 in 4-dimensional projective space. Iskovskih & Manin (1971) showed that all non-singular quartic threefolds are irrational, though some of them are unirational.

Examples

Burkhardt quartic
Igusa quartic

References

Iskovskih, V. A.; Manin, Ju. I. (1971), "Three-dimensional quartics and counterexamples to the Lüroth problem", Matematicheskii Sbornik, Novaya Seriya 86: 140–166, doi:10.1070/SM1971v015n01ABEH001536, MR 0291172

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