scholarly journals Ohsawa-Takegoshi Extension Theorem for Compact Kähler Manifolds and Applications

2017 ◽  
pp. 19-38 ◽  
Author(s):  
Junyan Cao
Keyword(s):  
Extension Theorem ◽  
Kähler Manifolds ◽  
Kahler Manifolds

Subadditivity of generalized Kodaira dimensions and extension theorems

2020 ◽  
Vol 31 (12) ◽  
pp. 2050098
Author(s):  
Xiangyu Zhou ◽  
Langfeng Zhu
Keyword(s):  
Extension Theorem ◽  
Kodaira Dimension ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Extension Theorems ◽  
Crucial Step ◽  
Ideal Sheaves ◽  
Multiplier Ideal ◽  
Singular Weights ◽  
Optimal Formula

In this paper, we introduce the notion of generalized Kodaira dimension with multiplier ideal sheaves, and prove the subadditivity of these generalized Kodaira dimensions for certain Kähler fibrations, which was originally obtained for Kodaira dimensions of algebraic fiber spaces by Kawamata and Viehweg. Our method is analytic and based on some new results in recent years. The crucial step in our proof is to prove an [Formula: see text] extension theorem for twisted pluricanonical sections on compact Kähler manifolds. Moreover, we also discuss the relation between two previous optimal [Formula: see text] extension theorems with singular weights on weakly pseudoconvex Kähler manifolds.

Sunada transplantation and isogeny of intermediate Jacobians of compact Kähler manifolds

2020 ◽  
Vol 72 (1) ◽  
pp. 127-147
Author(s):  
Carolyn Gordon ◽  
Eran Makover ◽  
Bjoern Muetzel ◽  
David Webb
Keyword(s):  
Kähler Manifolds ◽  
Kahler Manifolds

Holomorphically projective mappings between generalized m-parabolic Kähler manifolds

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4865-4873 ◽  
Author(s):  
Milos Petrovic
Keyword(s):  
Linear Systems ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Covariant Derivatives ◽  
Linearly Independent ◽  
Non Linear ◽  
Non Linear Systems ◽  
Curvature Tensors ◽  
Derivatives Of

Generalized m-parabolic K?hler manifolds are defined and holomorphically projective mappings between such manifolds have been considered. Two non-linear systems of PDE?s in covariant derivatives of the first and second kind for the existence of such mappings are given. Also, relations between five linearly independent curvature tensors of generalized m-parabolic K?hler manifolds with respect to these mappings are examined.

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