Singularities of Normal Quartic Surfaces I (char= 2)

We show, in this first part, that the maximal number of singular points a normal quartic surface $X \subset \mathbb {P}^{3}_{K}$ defined over an algebraically closed field K characteristic 2 is at most 16. produce examples with 14, respectively 12, and show that, under several geometric assumptions ( $\mathfrak S_{4}$ -symmetry, or behaviour Gauss map, structure tangent cone one P, separability/inseparability projection centre P), we can obtain smaller upper bounds for X.