Schemes of a finite projective plane and their extensions

Evdokimov, S.; Ponomarenko, I.

doi:10.1090/S1061-0022-09-01086-3

Schemes of a finite projective plane and their extensions
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by S. Evdokimov and I. Ponomarenko
Translated by: the authors

St. Petersburg Math. J. 21 (2010), 65-93

DOI: https://doi.org/10.1090/S1061-0022-09-01086-3

Published electronically: November 4, 2009

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Abstract:

There are several schemes (coherent configurations) associated with a finite projective plane $\mathcal {P}$. In the paper, a new scheme is constructed, which, in a sense, contains all of them. It turns out that this scheme coincides with the $2$-extension of the nonhomogeneous scheme of $\mathcal {P}$ and is uniquely determined up to similarity by the order $q$ of $\mathcal {P}$. Moreover, for $q\ge 3$, the rank of the scheme does not depend on $q$ and equals $416$. The results obtained have interesting applications in the theory of multidimensional extensions of schemes and similarities.

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