Non-normal purely log terminal centres in characteristic \(p \geqslant 3\)
type: Item
instance of: scholarly article
title: Non-normal purely log terminal centres in characteristic \(p \geqslant 3\)
zbMATH Open document ID: 1461.14021
author: Fabio Bernasconi
published in: European Journal of Mathematics
publication date: 2019-11-27T00:00:00Z
review text: The Minimal Model Program (MMP) is an important tool in the classification of higher dimensional algebraic varieties. In complete generality the MMP is still a conjecture but after the breakthrough result in [\textit{C. Birkar} et al., J. Am. Math. Soc. 23, No. 2, 405--468 (2010; Zbl 1210.14019)] the situation in characteristic zero is well understood. Over a field of characteristic \(p > 0\) instead, there are very few known results, in particular existence of flips is still an open conjecture. In [\textit{C. Hacon} and \textit{C. Xu}, J. Am. Math. Soc. 28, No. 3, 711--744 (2015; Zbl 1326.14032)] the authors were able to show that plt centers for threefolds are normal over algebraically closed fields of characteristic \(p > 5\). This allowed them to prove existence of pl-flips in that case. Unfortunately normality of plt centers does not holds in general: the first counterexample was found in [\textit{P. Cascini} and \textit{H. Tanaka}, Am. J. Math. 141, No. 4, 941--979 (2019; Zbl 1460.14040)] in characteristic two. In the paper under review, the author constructs new examples of non-normal plt centers for every prime \(p > 3\).
reviewed by: Diletta Martinelli
Mathematics Subject Classification ID: 14E30
Mathematics Subject Classification ID: 14J17
zbMATH DE Number: 7137472
zbMATH Keywords: MMP singularities
zbMATH Keywords: positive characteristic
zbMATH Keywords: Fano varieties
zbMATH Keywords: vanishing theorems
MaRDI profile type: Publication
full work available at URL: s40879-018-00310-7
OpenAlex ID: W2964305716
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DOI: 10.1007/S40879-018-00310-7
description: scientific article; zbMATH DE number 7137472