Caps on Elliptic Quadrics

G. L. Ebert (1985) constructed (qn + 1)-caps in PG(2n − 1, q), n even, which were the orbits of the subgroup of order qn + 1 of a cyclic Singer group of PG(2n − 1, q). This article shows that these caps are the intersection of n − 1 linearly independent elliptic quadrics of PG(2n − 1, q).