An embedding theorem of complete Kähler manifolds of positive Ricci curvature onto quasi-projective varieties
type: Item
instance of: scholarly article
title: An embedding theorem of complete Kähler manifolds of positive Ricci curvature onto quasi-projective varieties
zbMATH Open document ID: 0711.53057
DOI: 10.1007/BF01453581
author: Ngaiming Mok
published in: Mathematische Annalen
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164643
review text: It is well known that a compact Kähler manifold with positive Ricci curvature is projective algebraic. As a non compact version, the author proves the following Theorem. Let X be an n-dimensional complete Kähler manifold of positive Ricci curvature. Suppose for some base point \(x_ 0\) and some positive constants C and c we have (i) scalar curvature \(\leq C/d(x_ 0;x)^ 2\), \(\int_{x}Ric^ n<\infty\); (ii) \(Vol(B(x_ o;r))\geq cr^{2n}\), where \(d(x_ 0,x)\) denotes the geodesic distance and \(B(x_ 0;r)\) denotes the geodesic ball centered at \(x_ 0\) of radius r. Then, X is biholomorphic to a quasi-projective variety. Previously the author has proved the above theorem under the assumption that the holomorphic bisectional curvature is positive. The author follows a similar scheme of proof for the case of positive biholomorphic sectional curvature. However, he has needed much more arguments due to the lack of a single plurisubharmonic function for the general case.
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 51N35
zbMATH DE Number: 4169620
zbMATH Keywords: Kähler manifold
zbMATH Keywords: scalar curvature
zbMATH Keywords: quasi-projective variety
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4169620