We construct a new ovoid of the polar space arising from the Hermitian surface of $PG(3,q^2)$ with $q\geq 5$ odd. The automorphism group $\Gamma$ of such an ovoid has a normal cyclic subgroup $\Phi$ of order $\frac{1}{2}(q+1)$ such that $\Gamma/\Phi\cong PGL(2,q).$ Furthermore, $\Gamma$ has three orbits on the ovoid, one of size $q+1$ and two of size $\frac{1}{2}q(q-1)(q+1).$
Ovoids of the Hermitian Surface in Odd Characteristic
GIUZZI, Luca;
2003-01-01
Abstract
We construct a new ovoid of the polar space arising from the Hermitian surface of $PG(3,q^2)$ with $q\geq 5$ odd. The automorphism group $\Gamma$ of such an ovoid has a normal cyclic subgroup $\Phi$ of order $\frac{1}{2}(q+1)$ such that $\Gamma/\Phi\cong PGL(2,q).$ Furthermore, $\Gamma$ has three orbits on the ovoid, one of size $q+1$ and two of size $\frac{1}{2}q(q-1)(q+1).$File in questo prodotto:
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