Existence of flips and minimal models for 3-folds in char \(p\)
type: Item
instance of: scholarly article
zbMATH Open document ID: 1346.14040
author: Caucher Birkar
publication date: 2016-04-21T00:00:00Z
full work available at URL: https://arxiv.org/abs/1311.3098
full work available at URL: ens ann-sc 49 169-212.php
Mathematics Subject Classification ID: 14E30
Mathematics Subject Classification ID: 14J30
zbMATH DE Number: 6571732
zbMATH Keywords: minimal models
zbMATH Keywords: flips
zbMATH Keywords: 3-folds
MaRDI profile type: Publication
OpenAlex ID: W2962925489
arXiv ID: 1311.3098
DOI: 10.24033/ASENS.2279
title: Existence of flips and minimal models for 3-folds in char \(p\)
published in: Annales Scientifiques de l'École Normale Supérieure. Quatrième Série
review text: Let \((X,B)\) be a \(\mathbb Q\)-factorial pair defined over an algebraically closed field \(k\) of characteristic \(p>5\). In this paper, building on results of \textit{C. D. Hacon} and \textit{C. Xu} [J. Am. Math. Soc. 28, No. 3, 711--744 (2015; Zbl 1326.14032)], the author shows the following fundamental results: if \((X,B)\) is dlt and \(f:X\to Z\) is a flipping contraction, then the flip of \(f\) exists; if \((X,B)\) is klt and \(K_X+B\) is pseudo-effective then \((X,B)\) has a minimal model; if \((X,B)\) is klt and \(K_X+B\) is big then the pluricanonical ring \(R(K_X+B)\) is finitely generated.
reviewed by: Christopher Hacon
description: scientific article; zbMATH DE number 6571732