Veronesean embeddings of Hermitian unitals

Abstract

In this paper, we determine the Veronesean embeddings of Hermitian unitals, i.e., the representations of Hermitian unitals as points of a 7-dimensional projective space where the blocks are plane ovals. As an application, we derive that the following objects coincide: (1) the generic hyperplane sections of Hermitian Veroneseans in an 8-dimensional projective space, (2) the Grassmannians of the classical spreads of non-degenerate quadrics of Witt index 2 in a 5-dimensional projective space, (3) the sets of absolute points of trialities of Witt index 1. As a consequence, we prove that the set of absolute points of a triality without fixed lines, but with absolute points, determines the triality quadric and the triality itself uniquely.