Existence of the Kähler-Einstein metric on certain Fano complete intersections
type: Item
instance of: scholarly article
title: Existence of the Kähler-Einstein metric on certain Fano complete intersections
zbMATH Open document ID: 1244.14029
DOI: 10.1134/S0001434610090270
published in: Mathematical Notes
publication date: 2011-11-25T00:00:00Z
review text: The existence of Kähler-Einstein metric on Fano varieties is an important problem both in differential and in algebraic geometry. Thanks to the work of \textit{J. P. Demailly} and \textit{J. Kollár} [Ann. Sci. Éc. Norm. Supér. (4) 34, No. 4, 525--556 (2001; Zbl 0994.32021)], the existence of such a metric can be obtained via a lower bound on the global log canonical threshold of the variety. The paper under review follows this method and proves the existence of the metric for the general element of a class of Fano complete intersection satisfying some numerical constraint.
reviewed by: Massimiliano Mella
Mathematics Subject Classification ID: 14J45
Mathematics Subject Classification ID: 14E30
zbMATH DE Number: 5980697
zbMATH Keywords: Fano
zbMATH Keywords: complete intersection
zbMATH Keywords: log canonical threshold
zbMATH Keywords: Kähler--Einstein metric
author: A. V. Pukhlikov
MaRDI profile type: Publication
cites work: Birational geometry of algebraic varieties with a pencil of Fano complete intersections
cites work: Semi-continuity of complex singularity exponents and Kähler-Einstein metrics on Fano orbifolds
cites work: Multiplier ideal sheaves and Kähler-Einstein metrics of positive scalar curvature
cites work: On Kähler-Einstein metrics on certain Kähler manifolds with \(C_ 1(M)>0\)
cites work: Birational automorphisms of Fano hypersurfaces
cites work: Birationally rigid Fano complete intersections
cites work: Birational geometry of Fano direct products
cites work: Birationally rigid iterated Fano double covers
full work available at URL: s0001434610090270
OpenAlex ID: W2083967236
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description: scientific article; zbMATH DE number 5980697