On the multicanonical systems of quasi-elliptic surfaces

Abstract

We consider the multicanonical systems $|mK_{S}|$ of quasi-elliptic surfaces with Kodaira dimension 1 in characteristic 2. We show that for any $m \geq 6$ $|mK_{S}|$ gives the structure of quasi-elliptic fiber space, and 6 is the best possible number to give the structure for any such surfaces.