112 Lines on Smooth Quartic Surfaces (Characteristic 3)

rams, sławomir; schütt, matthias;

Over a field k of characteristic 3, we prove that there are no smooth quartic surfaces S ⊂ P3k with more than 112 lines. Moreover, the surface with 112 lines is projectively equivalent over ¯k to the Fermat quartic. As a key ingredient, we derive a characteristic-free upper bound for the number of lines met by a conic on a smooth quartic surface.