Lines on K3 quartic surfaces in characteristic 3

Abstract We investigate the number of straight lines contained in a K3 quartic surface X defined over an algebraically closed field characteristic 3. prove that if contains 112 lines, then is projectively equivalent to Fermat surface; otherwise, at most 67 lines. improve this bound 58 star (ie four distinct intersecting smooth point ). Explicit equations three 1-dimensional families surfaces with and 8 singular points 48 are provided.