On uniqueness of meromorphic mappings from complete Kähler manifold into ℙn(ℂ)

2020 ◽  
pp. 2150061
Author(s):  
Ha Huong Giang ◽  
Nguyen Thi Nhung
Keyword(s):  
Uniqueness Theorem ◽  
General Condition ◽  
General Position ◽  
Kähler Manifold ◽  
Meromorphic Mappings ◽  
Kahler Manifold ◽  
Complete Kähler Manifold

In this paper, we prove a uniqueness theorem for meromorphic mappings of a complete Kähler manifold [Formula: see text] into [Formula: see text] sharing hyperplanes in general position under a general condition that the codimension of the intersection of inverse images of any [Formula: see text] hyperplanes is at least two.

Uniqueness problem of meromorphic mappings of a complete Kähler manifold into a projective space

2020 ◽  
Vol 70 (4) ◽  
pp. 863-876
Author(s):  
Ha Huong Giang
Keyword(s):  
Projective Space ◽  
General Condition ◽  
General Position ◽  
Kähler Manifold ◽  
Uniqueness Problem ◽  
Uniqueness Theorems ◽  
Meromorphic Mappings ◽  
Kahler Manifold ◽  
Complete Kähler Manifold

AbstractIn this article, we prove a new generalization of uniqueness theorems for meromorphic mappings of a complete Kähler manifold M into ℙn(ℂ) sharing hyperplanes in general position with a general condition on the intersections of the inverse images of these hyperplanes.

scholarly journals A cup product lemma for continuous plurisubharmonic functions

2018 ◽  
Vol 10 (02) ◽  
pp. 263-287
Author(s):  
Terrence Napier ◽  
Mohan Ramachandran
Keyword(s):  
Plurisubharmonic Function ◽  
Kähler Manifold ◽  
Analytic Set ◽  
Plurisubharmonic Functions ◽  
Structure Sheaf ◽  
Compactly Supported ◽  
Cup Product ◽  
Kahler Manifold ◽  
Complete Kähler Manifold

A version of Gromov’s cup product lemma in which one factor is the (1, 0)-part of the differential of a continuous plurisubharmonic function is obtained. As an application, it is shown that a connected noncompact complete Kähler manifold that has exactly one end and admits a continuous plurisubharmonic function that is strictly plurisubharmonic along some germ of a [Formula: see text]-dimensional complex analytic set at some point has the Bochner–Hartogs property; that is, the first compactly supported cohomology with values in the structure sheaf vanishes.

UNIQUENESS THEOREM OF MEROMORPHIC MAPPINGS INTO ℙN (ℂ) SHARING 2N + 3 HYPERPLANES REGARDLESS OF MULTIPLICITIES

2009 ◽  
Vol 20 (06) ◽  
pp. 717-726 ◽  
Author(s):  
ZHIHUA CHEN ◽  
QIMING YAN
Keyword(s):  
Uniqueness Theorem ◽  
General Position ◽  
Meromorphic Mappings

In this paper, we prove a uniqueness theorem of meromorphic mappings from ℂn into ℙN(ℂ) sharing 2N + 3 hyperplanes in ℙN(ℂ) located in general position without counting multiplicities.

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