Abstract
Let . For each , Thas and Van Maldeghem constructed a -dimensional dual hyperoval in with , called the Veronesean dual hyperoval. A quotient of the Veronesean dual hyperoval with ambient space , denoted , is constructed by Taniguchi, using a generator of the Galois group Gal.
In this note, using the above generator for and a -dimensional vector subspace of over , we construct a quotient of the Veronesean dual hyperoval in in case is even. Moreover, we prove the following: for generators and of the Galois group Gal,
above (for ) is not isomorphic to ,
is isomorphic to for any -dimensional vector subspaces and of , and
is isomorphic to if and only if or .
Hence, we construct many new non-isomorphic quotients of the Veronesean dual hyperoval in .
Citation
Hiroaki Taniguchi. Satoshi Yoshiara. "New quotients of the $d$-dimensional Veronesean dual hyperoval in $\mathrm{PG}(2d+1,2)$." Innov. Incidence Geom. 12 151 - 165, 2011. https://doi.org/10.2140/iig.2011.12.151
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