Intersections of the Hermitian surface with irreducible quadrics in $PG(3,q^2)$, $q$ odd

Angela Aguglia, Luca Giuzzi

Published 2013-07-31, updated 2014-07-30Version 4

In $PG(3,q^2)$, with $q$ odd, we determine the possible intersection sizes of a Hermitian surface $\mathcal{H}$ and an irreducible quadric $\mathcal{Q}$ having the same tangent plane $\pi$ at a common point $P\in{\mathcal Q}\cap{\mathcal H}$.