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The cubic Segre variety in PG(5, 2)

Shaw, Ron ; Gordon, Neil A.

Designs, codes, and cryptography, 2009-05, Vol.51 (2), p.141-156 [Periódico revisado por pares]

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Título:
The cubic Segre variety in PG(5, 2)
Autor: Shaw, Ron ; Gordon, Neil A.
Assuntos: Circuits ; Coding and Information Theory ; Computer Science ; Cryptology ; Data Structures and Information Theory ; Discrete Mathematics in Computer Science ; Information and Communication
É parte de: Designs, codes, and cryptography, 2009-05, Vol.51 (2), p.141-156
Descrição: The Segre variety in PG(5, 2) is a 21-set of points which is shown to have a cubic equation Q ( x ) = 0. If T ( x , y , z ) denotes the alternating trilinear form obtained by completely polarizing the cubic polynomial Q , then the associate U # of an r -flat is defined to be and so is an s -flat for some s . Those lines L of PG(5, 2) which are singular , satisfying that is L # = PG(5.2), are shown to form a complete spread of 21 lines. For each r -flat its associate U # is determined. Examples are given of four kinds of planes P which are self-associate, P # = P , and three kinds of planes for which P , P # , P ## are disjoint planes such that P ### = P .
Editor: Boston: Springer US
Idioma: Inglês

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