On the multicanonical systems of quasi-elliptic surfaces

TL;DR

This paper investigates the properties of multicanonical systems on quasi-elliptic surfaces in characteristic 2, establishing that for m ≥ 6, these systems define a quasi-elliptic fiber space, with 6 being the minimal such number.

Contribution

It proves that for quasi-elliptic surfaces with Kodaira dimension 1 in characteristic 2, the multicanonical system |mK_S| induces a fiber space structure for all m ≥ 6, and 6 is optimal.

Findings

|mK_S| induces a fiber space for m ≥ 6

6 is the minimal number for such structure

Results specific to characteristic 2 surfaces

Abstract

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