On the dynamics of the line operator Λ{2},{3} on some arrangements of six lines

The operator Lambda ({2},{3}) acting on line arrangements is defined by associating to a line arrangement A, the line arrangement which is the union of the lines containing exactly three points among the double points of A. We say that six lines not tangent to a conic form an unassuming arrangement if the singularities of their union are only double points, but the dual line arrangement has six triple points, six 5-points and 27 double points. The moduli space of unassuming arrangements is the union of a point and a line. The image by the operator Lambda ({2},{3}) of an unassuming arrangement is again an unassuming arrangement. We study the dynamics of the operator Lambda( {2},{3}) on these arrangements and we obtain that the periodic arrangements are related to the Ceva arrangements of lines.