On the canonical bundle formula and log abundance in positive characteristic
type: Item
instance of: scholarly article
title: On the canonical bundle formula and log abundance in positive characteristic
zbMATH Open document ID: 1492.14026
author: Jakub Witaszek
published in: Mathematische Annalen
publication date: 2022-03-25T00:00:00Z
full work available at URL: https://arxiv.org/abs/1711.04380
review text: 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.
Mathematics Subject Classification ID: 14E30
Mathematics Subject Classification ID: 14E05
zbMATH DE Number: 7498340
zbMATH Keywords: canonical bundle formula
zbMATH Keywords: log abundance
zbMATH Keywords: positive characteristic
reviewed by: Christopher Hacon
MaRDI profile type: Publication
OpenAlex ID: W3179206330
arXiv ID: 1711.04380
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DOI: 10.1007/S00208-021-02231-5
description: scientific article