Geometric structures arising from generalized j-planes


We study translation planes constructed by Andr\'e net replacement on jj\cdots j-planes and derivation on jj\cdots j-planes. Then, we get to the conclusion that the family of non-Andr\'e jj\cdots j-planes is new, and thus so are their replaced and derived planes.
We also study a new way to construct translation planes by putting together two `halves' of planes that belong to two different jj\cdots j-planes. We show examples of planes of small order constructed this way.
Finally, we prove that using regular hyperbolic covers, jj\cdots j-planes induce partitions of Segre varieties by Veronesians (sometimes called flat flocks)

DOI Code: 10.1285/i15900932v29n2p1

Translation planes; Andrè nets; derivable nets; glat flocks; generalized j-planes

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