On p‐power freeness in positive characteristic

Abstract

In this note, we study base point freeness up to taking p-power, which we will call p-power freeness. We first establish some criteria for p-power freeness as analogues of criteria for semi-ampleness. We then apply these results to threedimensional birational geometry.

On the base point free theorem for klt threefolds in large characteristic

“…In a recent preprint [Tanb], H. Tanaka investigates freeness for Cartier divisors up to p-power in positive characteristic. Using the MMP for threefolds, he then shows a similar result of Theorem 1.3 for nef Cartier divisors on klt threefold log pairs over perfect fields of characteristic p > 5 up to taking p-powers (see [Tanb,Theorem 1.7]).…”