Curvature properties for moduli of canonically polarized manifolds -- an analogy to moduli of Calabi-Yau manifolds
type: Item
instance of: scholarly article
title: Curvature properties for moduli of canonically polarized manifolds -- an analogy to moduli of Calabi-Yau manifolds
zbMATH Open document ID: 1307.32020
author: Georg Schumacher
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2014-11-04T00:00:00Z
review text: The author studies the analogy between the moduli of canonically polarized varieties and Calabi-Yau manifolds, when these are equipped with Kähler-Einstein forms. Due to the absence of a Torelli-type theorem, the author constructs a Finsler metric in the orbifold sense. Among other things, the author produces a stronger inequality from the curvature formula which yields the negativity of the Finsler metric. This, in turn, implies a Kobayashi hyperbolicity of the moduli stack of canonically polarized varieties.
reviewed by: Vehbi Emrah Paksoy
Mathematics Subject Classification ID: 32Q25
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 6365763
zbMATH Keywords: canonically polarized manifolds
zbMATH Keywords: Finsler metric
zbMATH Keywords: moduli stack
zbMATH Keywords: Calabi-Yau manifolds
MaRDI profile type: Publication
full work available at URL: j.crma.2014.08.008
OpenAlex ID: W1996649739
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DOI: 10.1016/J.CRMA.2014.08.008
description: scientific article; zbMATH DE number 6365763