On the canonical bundle formula and log abundance in positive characteristic
The Kawamata-Kodaira canonical bundle formula is a key result in the birational geometry of complex projective varieties and it has found many important applications. In this paper, the author proves a weak positive characteristic version of this canonical bundle formula for fibrations of relative dimension one. Various interesting applications are given, including to the log non-vanishing conjecture for three-dimensional klt pairs over any algebraically closed field \(k\) of characteristic \(p > 5\), to the termination of any sequence of three-dimensional flips in the pseudo-effective case, and to the log abundance conjecture for threefolds over \(k\) when the nef dimension is not maximal.
scientific article