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 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.

On the first pontrjagin class of homotopy complex projective spaces

2012 ◽  
Vol 62 (3) ◽  
Author(s):  
Yasuhiko Kitada
Keyword(s):  
Projective Space ◽  
Smooth Manifold ◽  
Complex Projective Space ◽  
Projective Spaces ◽  
Homotopy Equivalent ◽  
Complex Projective Spaces ◽  
Pontrjagin Class ◽  
Complex Projective ◽  
Homotopy Complex

AbstractLet M 2n be a closed smooth manifold homotopy equivalent to the complex projective space ℂP(n). It is known that the first Pontrjagin class p 1(M) of M 2n has the form (n+1+24α(M))u 2 for some integer α(M) where u is a generator of H 2(M; ℤ). We prove that α(M) is even when n is even but not divisible by 64.

Stable homotopy types of stunted complex projective spaces

1973 ◽  
Vol 73 (3) ◽  
pp. 431-438 ◽  
Author(s):  
S. Feder ◽  
S. Gitler
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Projective Spaces ◽  
Stable Homotopy ◽  
Complex Dimension ◽  
Complex Projective Spaces ◽  
Homotopy Types ◽  
Complex Projective

Let CPn denote the complex projective space of complex dimension n. If k < n, CPk−1 is embedded as the (2k –1)-skeleton of CPn and we denote by , the stunted projective space, the quotient of CPn. by CPk−1.

scholarly journals The index of harmonic maps from surfaces to complex projective spaces

2020 ◽  
Vol 31 (09) ◽  
pp. 2050069
Author(s):  
J. Oliver
Keyword(s):  
Projective Space ◽  
Lower Bounds ◽  
Complex Projective Space ◽  
Harmonic Maps ◽  
Projective Spaces ◽  
Line Bundles ◽  
Complex Projective Spaces ◽  
Holomorphic Sections ◽  
Higher Genus ◽  
Complex Projective

We estimate the dimensions of the spaces of holomorphic sections of certain line bundles to give improved lower bounds on the index of complex isotropic harmonic maps to complex projective space from the sphere and torus, and in some cases from higher genus surfaces.

On projective spaces over two skew fields

1966 ◽  
Vol 62 (3) ◽  
pp. 395-398
Author(s):  
R. H. F. Denniston
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Classical Problem ◽  
Projective Spaces ◽  
The Other ◽  
Real Projective Space ◽  
Skew Fields ◽  
Complex Projective

Introduction. It is a classical problem to construct a complex projective space, using as ‘imaginary points’ objects of some kind from the geometry of real projective space. (The various solutions to this problem have been reviewed in a book by Coolidge ((1)).) The object of the present paper is to solve the corresponding problem for n-dimensional projective spaces over two skew fields, one being a second-rank extension of the other. The method used seems not to have been published before, even in connexion with the classical problem.

Non-Compact Complex Projective Space as a Phase Space

2020 ◽  
Vol 17 (5) ◽  
pp. 744-747
Author(s):  
E. Khastyan ◽  
H. Shmavonyan
Keyword(s):  
Phase Space ◽  
Projective Space ◽  
Complex Projective Space ◽  
Complex Projective

Branched Coverings and Minimal Free Resolution for Infinite-Dimensional Complex Spaces

2003 ◽  
Vol 10 (1) ◽  
pp. 37-43
Author(s):  
E. Ballico
Keyword(s):  
Projective Space ◽  
Projective Spaces ◽  
Free Resolution ◽  
Complete Intersections ◽  
Vanishing Theorem ◽  
Sheaf Cohomology ◽  
Minimal Free Resolution ◽  
Branched Coverings ◽  
Infinite Dimensional ◽  
Complex Spaces

Abstract We consider the vanishing problem for higher cohomology groups on certain infinite-dimensional complex spaces: good branched coverings of suitable projective spaces and subvarieties with a finite free resolution in a projective space P(V ) (e.g. complete intersections or cones over finitedimensional projective spaces). In the former case we obtain the vanishing result for H 1. In the latter case the corresponding results are only conditional for sheaf cohomology because we do not have the corresponding vanishing theorem for P(V ).

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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