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Over a field k of characteristic 3, we prove that there are no smooth quarticsurfaces S in IP^3 with more than 112 lines. Moreover, the surface with 112lines is projectively equivalent over k-bar to the Fermat quartic. As a keyingredient, we derive a characteristic free upper bound for the number of linesmet by a quadric on a smooth quartic surface.

112 lines on smooth quartic surfaces (characteristic 3)