On the deformation theory of Calabi-Yau structures in strongly pseudo-convex manifolds
type: Item
instance of: scholarly article
title: On the deformation theory of Calabi-Yau structures in strongly pseudo-convex manifolds
zbMATH Open document ID: 1209.32013
author: Alireza Bahraini
published in: Bulletin of the Brazilian Mathematical Society. New Series
publication date: 2010-10-26T00:00:00Z
review text: Generalizing the Bogomolov-Tian-Todorov theorem, the author proves that on a strongly pseudoconvex Calabi-Yau manifold the deformation theory of Calabi-Yau structures is unobstructed, and the moduli space can be identified with the Kohn-Rossi cohomology \(H^{1,1}\). To prove unobstructedness, he constructs a formal power series solution and then shows that it converges. He claims that this convergence was previously unknown, but it follows for example from the proof of Kuranishi's theorem on the deformation of complex structures.
reviewed by: Valentino Tosatti
Mathematics Subject Classification ID: 32Q25
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53C26
Mathematics Subject Classification ID: 14J32
Mathematics Subject Classification ID: 32G05
zbMATH DE Number: 5805931
zbMATH Keywords: strongly pseudo-convex manifolds
zbMATH Keywords: deformation theory
zbMATH Keywords: Calabi-Yau manifolds
MaRDI profile type: Publication
full work available at URL: s00574-010-0019-7
OpenAlex ID: W2079280478
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cites work: On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
DOI: 10.1007/S00574-010-0019-7
description: scientific article; zbMATH DE number 5805931