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 ≥ 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.