Patakfalvi, ZsoltSchweizer, Ursina2021-08-102021-08-102021-08-10202110.5075/epfl-thesis-8785https://infoscience.epfl.ch/handle/20.500.14299/180491While over fields of characteristic at least 5, a normal, projective and Gorenstein del Pezzo surface is geometrically normal, this does not hold for characteristic 2 and 3. There is no characterization of all such non-geometrically normal surfaces, but there is a complete characterization of all possible surfaces that can arise as the normalization of the base change to the algebraic closure of the base field. In four of these instances, for a given normalization, we describe the construction of such a non-geometrically normal surface.enBirational GeometryDel Pezzo SurfacesDu Val SingularitiesGeometric Non-NormalityPositive Characteristicthesis::doctoral thesis