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Mat. Zametki, 2008, Volume 84, Issue 1, Pages 40–47 (Mi mz4030)  

The Unirationality of Quartics over Nonclosed Fields Revisited

N. F. Zak

Central Bank of the Russian Federation

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

DOI: https://doi.org/10.4213/mzm4030

Full text: PDF file (462 kB)
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English version:
Mathematical Notes, 2008, 84:1, 38–44

Bibliographic databases:

UDC: 512.626
Received: 18.07.2007
Revised: 03.02.2008

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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