Geodesic
The Unirationality of Quartics over Nonclosed Fields Revisited
Matematičeskie zametki, Tome 84 (2008) no. 1, pp. 40-47

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Examples of smooth fourth-degree hypersurfaces which are unirational over an algebraically nonclosed field $\Bbbk$ and contain no straight lines defined over $Bbbk$ are given. A method for proving the unirationality of quartics is suggested, which, unlike other methods, does not use linear spaces contained in the quartics.
Mots-clés : unirational quartic, birational projection.
Keywords: quartic over an algebraically nonclosed field, unirational variety, irreducible hypersurface, Plucker embedding 
N. F. Zak. The Unirationality of Quartics over Nonclosed Fields Revisited. Matematičeskie zametki, Tome 84 (2008) no. 1, pp. 40-47. http://geodesic.mathdoc.fr/item/MZM_2008_84_1_a2/
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