### Characterisations of ovoids of PG(3,q) by plane section

Matthew Brown
*Ghent*

An *ovoid* of the projective space PG(*3,q*) is a set of
*q^2+1* points, no three of which are collinear. An ovoid has the
properties that at each point of the ovoid there is a unique tangent
plane and any other plane of PG(*3,q*) meets the ovoid in an
*oval* (a set of *q+1* points, no three of which are collinear).
The classical model of the ovoid is a non-singular quadric of elliptic
type and the only other known construction is due to Tits in 1960. I
will speak on my work which includes two characterisation results for
ovoids where the hypothesis is on a *single* plane section of the
ovoid. In particular an ovoid containing a single conic will be shown
to the be the elliptic quadric; and an ovoid containing a pointed
conic will be shown to be either an elliptic quadric in
PG(*3,4*) or a Tits ovoid in PG(*3,8*).