On the extension theorem of Hwang and Mok
type: Item
instance of: scholarly article
title: On the extension theorem of Hwang and Mok
zbMATH Open document ID: 1406.14030
author: Jan Gutt
published in: Journal für die Reine und Angewandte Mathematik
publication date: 2018-10-10T00:00:00Z
review text: Let \(X\) and \(X^{\prime}\) be Fano manifolds of Picard number 1. Let \(U \subset X\) and \(U^{\prime} \subset X^{\prime}\) be open connected subsets and \(\phi : U \rightarrow U^{\prime}\) be a biholomorphism. In [\textit{J.-M. Hwang} and \textit{N. Mok}, J. Math. Pures Appl. (9) 80, No. 6, 563--575 (2001; Zbl 1033.32013)] conditions were obtained under which the map \(\phi\) extends to a biholomorphism \(\bar{\phi} : X \rightarrow X^{\prime}\). The methods used in that paper were coming both from algebraic geometry and complex differential geometry. This paper obtains a characteristic free analog of the aforementioned result of Hwang and Mok.
reviewed by: Nikolaos Tziolas
Mathematics Subject Classification ID: 14J45
Mathematics Subject Classification ID: 14E05
Mathematics Subject Classification ID: 14D15
zbMATH DE Number: 6950101
zbMATH Keywords: Fano varieties
zbMATH Keywords: Picard number 1
zbMATH Keywords: birational maps
zbMATH Keywords: extension
zbMATH Keywords: formal arcs
MaRDI profile type: Publication
full work available at URL: crelle-2015-0106
OpenAlex ID: W2327080197
cites work: Q4040891
cites work: Q2551490
cites work: Q3151798
cites work: Rigidity of irreducible Hermitian symmetric spaces of the compact type under Kähler deformation
cites work: Cartan-Fubini type extension of holomorphic maps for Fano manifolds of Picard number 1.
cites work: Geometry Associated with Semisimple Flat Homogeneous Spaces
cites work: Parabolic subgroups with Abelian unipotent radical
DOI: 10.1515/CRELLE-2015-0106
description: scientific article; zbMATH DE number 6950101