On the canonical bundle formula and log abundance in positive characteristic
Abstract
We show that a weak version of the canonical bundle formula holds for fibrations of relative dimension one. We provide various applications thereof, for instance, using the recent result of Xu and Zhang, we prove the log non-vanishing conjecture for three-dimensional klt pairs over any algebraically closed field of characteristic . We also show the log abundance conjecture for threefolds over when the nef dimension is not maximal, and the base point free theorem for threefolds over the algebraic closure of any finite field of characteristic .
Keywords
Cite
@article{arxiv.1711.04380,
title = {On the canonical bundle formula and log abundance in positive characteristic},
author = {Jakub Witaszek},
journal= {arXiv preprint arXiv:1711.04380},
year = {2018}
}
Comments
33 pages; the article has been substantially changed and the results are stronger: we now show log non-vanishing for all three-dimensional klt pairs of characteristic $p>5$, and log abundance when the nef dimension is not maximal. Further, we corrected a mistake in Lemma 4.3(1) (now Lemma 5.1(1)): the effectivity of adjoint divisors on surfaces holds only up to numerical equivalence