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Matematicheskie Zametki, 2008, Volume 84, Issue 1, Pages 40–47
DOI: https://doi.org/10.4213/mzm4030 (Mi mzm4030) 		 
The Unirationality of Quartics over Nonclosed Fields Revisited

N. F. Zak

Central Bank of the Russian Federation
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DOI: https://doi.org/10.4213/mzm4030
Abstract: 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.
Keywords: unirational quartic, quartic over an algebraically nonclosed field, unirational variety, irreducible hypersurface, Plucker embedding, birational projection.
Received: 18.07.2007
Revised: 03.02.2008
English version:
Mathematical Notes, 2008, Volume 84, Issue 1, Pages 38–44
DOI: https://doi.org/10.1134/S0001434608070031
Bibliographic databases:
UDC: 512.626
Language: Russian
Citation: N. F. Zak, “The Unirationality of Quartics over Nonclosed Fields Revisited”, Mat. Zametki, 84:1 (2008), 40–47; Math. Notes, 84:1 (2008), 38–44
Citation in format AMSBIB
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