scholarly journals Holomorphic Mappings into Projective Space with Lacunary Hyperplanes

1973 ◽  
Vol 50 ◽  
pp. 199-216 ◽  
Author(s):  
Peter Kiernan ◽  
Shoshichi Kobayashi
Keyword(s):  
Projective Space ◽  
General Position ◽  
Complex Projective Space ◽  
Complex Space ◽  
General Setting ◽  
Holomorphic Mappings ◽  
Complex Projective

In this note, we shall examine some results of Bloch [2] and Cartan [3] concerning complex projective space minus hyperplanes in general position. The purpose is to restate their results in a more general setting by using the intrinsic pseudo-distance defined on a complex space [16] and the concept of tautness introduced by Wu in [18]. In the process we shall generalize some results of Dufresnoy [4] and Fuj imoto [7].

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.

Einstein-Kaehler Manifolds Immersed in a Complex Projective Space

1976 ◽  
Vol 28 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Hisao Nakaga
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Local Version ◽  
Kaehler Manifold ◽  
Kaehler Manifolds ◽  
Simply Connected ◽  
Complex Projective

A Kaehler manifold of constant holomorphic curvature is called a complex space form. By a Kaehler submanifold we mean a complex submanifold with the induced Kaehler metric. B. Smyth [5] has studied a complete Einstein- Kaehler hypersurface in a complete and simply connected complex space form and classified completely the hypersurface. The local version of this result has been shown to be true by S. S. Chern [1], and partially by T. Takahashi [6] independently.

scholarly journals Uniqueness theorem for holomorphic mappings on annuli sharing few hyperplanes

2021 ◽  
Vol 73 (2) ◽  
pp. 249-260
Author(s):  
Ha Huong Giang
Keyword(s):  
Projective Space ◽  
Uniqueness Theorem ◽  
General Condition ◽  
Complex Projective Space ◽  
Holomorphic Mappings ◽  
Complex Projective

UDC 517.5 We prove a uniqueness theorem of linearly nondegenerate holomorphic mappings from annulus to complex projective space with different multiple values and a general condition on the intersections of the inverse images of these hyperplanes.

scholarly journals A Theorem on Analytic Mappings of Complex Manifolds

1966 ◽  
Vol 27 (2) ◽  
pp. 543-557 ◽  
Author(s):  
Minoru Kurita
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Complex Space ◽  
Main Idea ◽  
Complex Manifolds ◽  
Normal Contact ◽  
Contact Metric Structure ◽  
Complex Projective ◽  
Analytic Mappings

We prove in this paper a theorem on analytic mappings of the complex space Cn into the complex projective space Pn. The theorem is closely related to that of S. S. Chern in [1], and the main idea of the proof is the same with the latter, though the calculations are rather different. The background of our calculation is the normal contact metric structure which was found by S. Sasaki and Y. Hatakeyama [4].

scholarly journals Koszul property for points in projective spaces

2001 ◽  
Vol 89 (2) ◽  
pp. 201 ◽  
Author(s):  
Aldo Conca ◽  
Ngô Viêt Trung ◽  
Giuseppe Valla
Keyword(s):  
Projective Space ◽  
General Position ◽  
Complex Projective Space ◽  
Projective Spaces ◽  
Free Resolution ◽  
General Linear ◽  
Coordinate Ring ◽  
Koszul Property ◽  
Complex Projective

A graded $K$-algebra $R$ is said to be Koszul if the minimal $R$-free graded resolution of $K$ is linear. In this paper we study the Koszul property of the homogeneous coordinate ring $R$ of a set of $s$ points in the complex projective space $\boldsymbol P^n$. Kempf proved that $R$ is Koszul if $s\leq 2n$ and the points are in general linear position. If the coordinates of the points are algebraically independent over $\boldsymbol Q$, then we prove that $R$ is Koszul if and only if $s\le 1 +n + n^2/4$. If $s\le 2n$ and the points are in linear general position, then we show that there exists a system of coordinates $x_0,\dots,x_n$ of $\boldsymbol P^n$ such that all the ideals $(x_0,x_1,\dots,x_i)$ with $0\le i \le n$ have a linear $R$-free resolution.

scholarly journals From surfaces in the 5-sphere to 3-manifolds in complex projective 3-space

2002 ◽  
Vol 66 (3) ◽  
pp. 465-475 ◽  
Author(s):  
J. Bolton ◽  
C. Scharlach ◽  
L. Vrancken
Keyword(s):  
Projective Space ◽  
Minimal Surface ◽  
Complex Projective Space ◽  
Lagrangian Submanifold ◽  
3 Dimensional ◽  
Ellipse Of Curvature ◽  
Complex Projective

In a previous paper it was shown how to associate with a Lagrangian submanifold satisfying Chen's equality in 3-dimensional complex projective space, a minimal surface in the 5-sphere with ellipse of curvature a circle. In this paper we focus on the reverse construction.

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