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 
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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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