Algebraic dependences of meromorphic mappings sharing moving hyperplanes without counting multiplicities

2017 ◽  
Vol 10 (03) ◽  
pp. 1750040 ◽  
Author(s):  
Le Ngoc Quynh
Keyword(s):  
Projective Space ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Meromorphic Mappings ◽  
Counting Multiplicity

This paper deals with the multiple values and algebraic dependences problem of meromorphic mappings sharing moving hyperplanes in projective space. We give some algebraic dependences theorems for meromorphic mappings sharing moving hyperplanes without counting multiplicity, where all zeros with multiplicities more than a certain number are omitted. Basing on these results, some unicity theorems regardless of multiplicity for meromorphic mappings in several complex variables are given. These results are extensions and strong improvements of some recent results.

scholarly journals Normal families of meromorphic mappings of several complex variables for moving hypersurfaces in a complex projective space

2015 ◽  
Vol 217 ◽  
pp. 23-59
Author(s):  
Gerd Dethloff ◽  
Do Duc Thai ◽  
Pham Nguyen Thu Trang
Keyword(s):  
Projective Space ◽  
Recent Work ◽  
Complex Projective Space ◽  
Sufficient Conditions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Normal Families ◽  
Meromorphic Mappings ◽  
Meromorphic Maps ◽  
Complex Projective

AbstractThe main aim of this article is to give sufficient conditions for a family of meromorphic mappings of a domainDin ℂninto ℙN(ℂ) to be meromorphically normal if they satisfy only some very weak conditions with respect to moving hypersurfaces in ℙN(ℂ), namely, that their intersections with these moving hypersurfaces, which moreover may depend on the meromorphic maps, are in some sense uniform. Our results generalize and complete previous results in this area, especially the works of Fujimoto, Tu, Tu-Li, Mai-Thai-Trang, and the recent work of Quang-Tan.

scholarly journals Normal families of meromorphic mappings of several complex variables for moving hypersurfaces in a complex projective space

2015 ◽  
Vol 217 ◽  
pp. 23-59 ◽  
Author(s):  
Gerd Dethloff ◽  
Do Duc Thai ◽  
Pham Nguyen Thu Trang
Keyword(s):  
Projective Space ◽  
Recent Work ◽  
Complex Projective Space ◽  
Sufficient Conditions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Normal Families ◽  
Meromorphic Mappings ◽  
Meromorphic Maps ◽  
Complex Projective

AbstractThe main aim of this article is to give sufficient conditions for a family of meromorphic mappings of a domain D in ℂn into ℙN(ℂ) to be meromorphically normal if they satisfy only some very weak conditions with respect to moving hypersurfaces in ℙN(ℂ), namely, that their intersections with these moving hypersurfaces, which moreover may depend on the meromorphic maps, are in some sense uniform. Our results generalize and complete previous results in this area, especially the works of Fujimoto, Tu, Tu-Li, Mai-Thai-Trang, and the recent work of Quang-Tan.

scholarly journals Holomorphic mappings into the complex projective space with moving hypersurfaces

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 955-962
Author(s):  
Liu Yang
Keyword(s):  
Projective Space ◽  
Recent Work ◽  
General Position ◽  
Complex Projective Space ◽  
Type Theorem ◽  
Complex Variables ◽  
Holomorphic Mappings ◽  
Several Complex Variables ◽  
Picard Type Theorem ◽  
Complex Projective

Motivated by Eremenko?s accomplisshment of a Picard-type theorem [Period Math Hung. 38 (1999), pp.39-42.], we study the normality of families of holomorphic mappings of several complex variables into PN(C) for moving hypersurfaces located in general position. Our results generalize and complete previous results in this area, especially the works of Dufresnoy, Tu-Li, Tu-Cao, Yang-Fang-Pang and the recent work of Ye-Shi-Pang.

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