Abstract

Giuzzi (2006) and Donati and Duranti (2008) determined the structure of the intersection of two Hermitian surfaces of $PG\left(3,q^2\right)$ under the hypotheses that in the pencil they generate there is at least one degenerate surface. Aguglia, Cossidente and Ebert (2005) and Donati and Duranti (2008) showed that under suitable hypotheses the intersection of two Hermitian surfaces generating a non-degenerate pencil is a pseudo-regulus. Here we completely determine all possible intersection configurations for two Hermitian surfaces of $PG\left(3,q^2\right)$ generating a non-degenerate pencil.

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