Abstract
AbstractOvoids of the parabolic quadric Q(6, q) of $$\textrm{PG}(6,q)$$
PG
(
6
,
q
)
have been largely studied in the last 40 years. They can only occur if q is an odd prime power and there are two known families of ovoids of Q(6, q), the Thas-Kantor ovoids and the Ree-Tits ovoids, both for q a power of 3. It is well known that to any ovoid of Q(6, q) two polynomials $$f_1(X,Y,Z)$$
f
1
(
X
,
Y
,
Z
)
, $$f_2(X,Y,Z)$$
f
2
(
X
,
Y
,
Z
)
can be associated. In this paper we classify ovoids of Q(6, q) with $$\max \{\deg (f_1),\deg (f_2)\}<(\frac{1}{6.3}q)^{\frac{3}{13}}-1$$
max
{
deg
(
f
1
)
,
deg
(
f
2
)
}
<
(
1
6.3
q
)
3
13
-
1
.
Funder
Università degli Studi di Perugia
Publisher
Springer Science and Business Media LLC