A Note on Fano Configurations in the Projective Space PG(5,2)

Year 2021, Volume: 9 Issue: 1, 190 - 192, 28.04.2021

Ziya Akça , Abdilkadir Altıntaş

Abstract

Let $n\geq $ $2$ and let $U_{j}\mid j\in J$, with $|J|=n^{2}+n+1$, be a set of disjoint subspaces (of the same dimension) of some finite projective space $PG(N,q)$ with the property that the number of such subspaces in the span of any two such subspaces is always $n+1$ and the intersection of any two different such spans is always a subspace $U_{j}$ (so we have a projective plane of order $n$ with point set $U_{j}\mid j\in J.$) In this work we search for Fano configurations in PG(5,2) whose lines are 3-spaces and points are lines.

Keywords

"Projective spaces", "Fano Plane", " Fano Axiom"

Supporting Institution

This work was supported by the Scientiic Research Projects Commission of Eskisehir Osmangazi University .

Project Number

2019-2542

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