Abstract

A new class of translation planes of order $4^3$ is constructed and studied. These planes are a generalization of the $j$-planes discovered by Johnson, Pomareda and Wilke. These $j,k$-planes may be André replaced and the $j,k$-planes and the planes obtained by André replacement may be derived. There are thirteen new planes constructed and classified. Using ‘regular hyperbolic covers’, there are some new constructions of flat flocks of Segre varieties by Veronesians.

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Mathematical Subject Classification 2000

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