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 Izv. Vyssh. Uchebn. Zaved. Mat., 2018, Number 11, Pages 15–26 (Mi ivm9409)

Geometric construction of linear complex of planes of $B_3$ type

A. N. Makokha

North-Caucasian Federal University, 1 Pushkin str., 355009, Stavropol Russia

Abstract: Using invariant geometric images of a trivector of type $(884; 400)$, we construct its basic group of automorphisms. We formulate and prove a theorem on necessary and sufficient conditions for determining of all planes of a linear complex associated with a trivector of a given type accurate to linear transformations of its automorphism group. In the process of proving of the theorem, we find all kinds of singular lines and for their nonsingular lines construct their polar hyperplanes.

Keywords: trivector, singulars points of the first and second kinds, singulars and non-singulars directs, singulars subspaces, polar hyperplane, automorphism group of a trivector.

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UDC: 514.743

Citation: A. N. Makokha, “Geometric construction of linear complex of planes of $B_3$ type”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 11, 15–26

Citation in format AMSBIB
\Bibitem{Mak18} \by A.~N.~Makokha \paper Geometric construction of linear complex of planes of $B_3$ type \jour Izv. Vyssh. Uchebn. Zaved. Mat. \yr 2018 \issue 11 \pages 15--26 \mathnet{http://mi.mathnet.ru/ivm9409}