Lower bounds of Tian's invariant under toric invariances
type: Item
instance of: scholarly article
title: Lower bounds of Tian's invariant under toric invariances
zbMATH Open document ID: 1209.32012
author: Adnène Ben Abdesselem
author: Malek Filali
published in: Bulletin des Sciences Mathématiques
publication date: 2010-09-27T00:00:00Z
review text: This paper studies the geometry of Kähler potentials on a family of high-dimensional Fano manifolds. More precisely, the authors consider some explicit Fano manifolds which are projective bundles over a complex projective space, which generalize the blow up of complex projective space at one point and also generalize a famous construction of \textit{E. Calabi} [Ann. Math. Stud. 102, 259--290 (1982; Zbl 0487.53057)]. For each such manifold, they fix a finite group \(G\) of automorphisms and they give a lower bound for \textit{G. Tian}'s \(\alpha\)-invariant [Invent. Math. 89, 225--246 (1987; Zbl 0599.53046)] relative to \(G\). This is achieved via a careful study of \(G\)-invariant almost plurisubharmonic functions on these manifolds by explicitly constructing a function bounding below all of these, following the methods developed in [\textit{A. Ben Abdesselem}, Bull. Sci. Math. 130, 341--353 (2006; Zbl 1103.53042)]. Note that the \(\alpha\)-invariant of all toric Fano manifolds has been computed by \textit{J. Song} [Am. J. Math. 127, No.~6, 1247--1259 (2005; Zbl 1088.32012)].
reviewed by: Valentino Tosatti
Mathematics Subject Classification ID: 32Q20
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 14J45
zbMATH DE Number: 5791951
zbMATH Keywords: alpha-invariant
zbMATH Keywords: plurisubharmonic function
MaRDI profile type: Publication
full work available at URL: j.bulsci.2010.04.001
OpenAlex ID: W1981633465
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DOI: 10.1016/J.BULSCI.2010.04.001
description: scientific article; zbMATH DE number 5791951