Translation ovoids of unitary polar spaces

Abstract

Abstract An ovoid of a finite classical polar space is a set of points having exactly one point in common with every generator. An ovoid is a translation ovoid with respect to one of its points if it admits a collineation group fixing all totally isotropic lines through the point and acting regularly on the remaining points of the ovoid. Lunardon and Polverino proved in [11] that Q+(3; q), Q(4; q) and Q+(5; q) are the only finite orthogonal polar spaces having translation ovoids. In this paper we prove that H(3; q2) is the only finite unitary polar space having translation ovoids. We also prove that translation groups of ovoids of H(3; q2) contain only linear collineations.