A remark on toric foliations
type: Item
instance of: scholarly article
title: A remark on toric foliations
zbMATH Open document ID: 1543.14036
author: Osamu Fujino
author: Hiroshi Sato
published in: Archiv der Mathematik
publication date: 2024-05-13T00:00:00Z
review text: A toric foliation \(\mathcal{F}\) on a toric variety \(X\) is a nonzero saturated subsheaf \(\mathcal{F}\subseteq \mathcal{T}_X\) that is torus equivariant and closed under the Lie bracket, where \(\mathcal{T}_X\) is the tangent sheaf of \(X\). In the paper under review, the author proves that, for a projective \(\mathbb{Q}\)-factorial toric variety, the length of any extremal ray with respect to a toric foliation \(\mathcal{F}\) does not exceed \(r(\mathcal{F})+1\) where \(r(\mathcal{F})\) is the rank of \(\mathcal{F}\); moreover, if \(\mathcal{F}\) has an extremal ray whose length is greater than \(r(\mathcal{F})\), then the associated extremal contraction is a projective space bundle and \(\mathcal{F}\) is the relative tangent sheaf of the extremal contraction and thus locally free.
reviewed by: Guolei Zhong
Mathematics Subject Classification ID: 14M25
Mathematics Subject Classification ID: 14E30
Mathematics Subject Classification ID: 32S65
zbMATH DE Number: 7846263
zbMATH Keywords: toric varieties
zbMATH Keywords: foliations
zbMATH Keywords: extremal rays
zbMATH Keywords: projective space bundles
MaRDI profile type: Publication
cites work: Toric varieties
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cites work: Equivariant completions of toric contraction morphisms
cites work: Introduction to the toric Mori theory
cites work: Introduction to the Mori program
cites work: Q3453584
cites work: Q3688496
cites work: Toric foliated minimal model program
DOI: 10.1007/S00013-024-01991-1
description: scientific article; zbMATH DE number 7846263