Simultaneous desingularizations of Calabi-Yau and special Lagrangian 3-folds with conical singularities. I: the gluing construction
type: Item
instance of: scholarly article
title: Simultaneous desingularizations of Calabi-Yau and special Lagrangian 3-folds with conical singularities. I: the gluing construction
zbMATH Open document ID: 1188.53052
author: Yat-Ming Chan
published in: Annals of Global Analysis and Geometry
publication date: 2009-07-13T00:00:00Z
review text: The author extends a previous result on desingularizing conically singular Calabi-Yau manifolds. Let \(M_{0}\) be a Calabi-Yau 3-fold with isolated concial singularities at \(\{x_{i} : 1 \leq i \leq n \}\), and let \(N_{0}\) be a special Langrangian 3-manifold in \(M_{0}\) with conical singularities at the same points \(\{x_{i} : 1 \leq i \leq n \}\). Let \(Y_{i}\) be an asymptotically canonical Calabi-Yau 3-fold , and Let \(L_{i}\) be an asymptotically canonical special Lagrangian 3-fold in \(Y_{i}\). The author glues in rescaled copies of \(Y_{i}\) and \(L_{i}\) simultaneously to \(M_{0}\) and \(N_{0}\) at \(x_{i}\) respectively and deforms both together to achieve a smooth Calabi-Yau manifold. He expects that this method will produce new examples of compact special Langrangian 3-folds in compact Calabi-Yau 3-folds. In a sequel to his paper with the same main title the author applies the results of this paper to obtain examples. This paper fits into a comprehensive program developed by D. Joyce.
reviewed by: Patrick Eberlein
Mathematics Subject Classification ID: 53C38
zbMATH DE Number: 5577697
zbMATH Keywords: Calabi-Yau manifolds
zbMATH Keywords: special Lagrangian submanifolds
zbMATH Keywords: conical singularities
zbMATH Keywords: asymptotically conical
MaRDI profile type: Publication
full work available at URL: s10455-008-9124-x
OpenAlex ID: W2158566077
cites work: DESINGULARIZATIONS OF CALABI–YAU 3-FOLDS WITH A CONICAL SINGULARITY
cites work: DESINGULARIZATIONS OF CALABI-YAU 3-FOLDS WITH CONICAL SINGULARITIES. II. THE OBSTRUCTED CASE
cites work: Simultaneous desingularizations of Calabi-Yau and special Lagrangian 3-folds with conical singularities. II: Examples
cites work: Simultaneous resolution of threefold double points
cites work: Calibrated geometries
cites work: Q4523708
cites work: Special Lagrangian submanifolds with isolated conical singularities. V: Survey and applications.
cites work: Special Lagrangian submanifolds with isolated conical singularities. I: Regularity
cites work: Special Lagrangian submanifolds with isolated conical singularities. II: Moduli spaces
cites work: Special Lagrangian submanifolds with isolated conical singularities. III: Desingularization, the unobstructed case
cites work: Special Lagrangian submanifolds with isolated conical singularities. IV: Desingularization, obstructions and families
cites work: Q4722903
cites work: Corrigenda to: Introduction to Symplectic Topology
cites work: Mirror symmetry is \(T\)-duality
cites work: Q4840444
cites work: On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
DOI: 10.1007/S10455-008-9124-X
description: scientific article; zbMATH DE number 5577697