A Combinatorial Characterazition of the Fermat Cubic Surface in Characteristic 2

Author: Homma M.  

Publisher: Springer Publishing Company

ISSN: 0046-5755

Source: Geometriae Dedicata, Vol.64, Iss.3, 1997-03, pp. : 311-318

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Abstract

We study a particular geometry in characteristic 2. Let X be a cubic surface obtained from bP2by means of blowing up with centers P_{1} , ldots, P_{6} . We prove that X is projectively equivalent to the Fermat cubic surface with equation Sigma x_{i}^{3}= 0if and only if each point of P_{1} , ldots, P_{6} is the nucleus of the conic passing through the remaining five points.