Discrepancies of non-\(\mathbb Q\)-Gorenstein varieties
type: Item
instance of: scholarly article
title: Discrepancies of non-\(\mathbb Q\)-Gorenstein varieties
zbMATH Open document ID: 1260.14042
author: Stefano Urbinati
published in: Michigan Mathematical Journal
publication date: 2013-03-05T00:00:00Z
full work available at URL: https://arxiv.org/abs/1001.2930
full work available at URL: https://projecteuclid.org/euclid.mmj/1339011527
review text: The author investigates the singularities of non-\(\mathbb Q\)-Gorenstein varieties. The case of \(\mathbb Q\)-Gorenstein singularities has been extensively studied in the context of the minimal model program and is by now well understood. A new approach extending the definitions of canonical singularities, klt singularities and multiplier ideals to the non-\(\mathbb Q\)-Gorenstein setting was introduced in the recent paper [\textit{T. de Fernex} and \textit{C. D. Hacon}, Compos. Math. 145, No. 2, 393--414 (2009; Zbl 1179.14003)]. In the paper under review, the author shows that: 1) the relative canonical divisor of a klt singularity always has rational valuations and gives examples of a non-klt non-\(\mathbb Q\)-Gorenstein singularity whose relative canonical divisor has irrational valuations, 2) there are canonical singularities that are not klt, 3) canonical models have canonical singularities, and 4) if \(X\) has a klt or an isolated singularity then the jumping numbers are discrete.
Mathematics Subject Classification ID: 14J17
Mathematics Subject Classification ID: 14F18
Mathematics Subject Classification ID: 14B05
zbMATH DE Number: 6141578
zbMATH Keywords: singularities
zbMATH Keywords: non-\(\mathbb Q\)-Gorenstein varieties
reviewed by: Christopher Hacon
MaRDI profile type: Publication
OpenAlex ID: W3105261754
arXiv ID: 1001.2930
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DOI: 10.1307/MMJ/1339011527
description: scientific article