scholarly journals Families of holomorphic maps into the projective space omitting some hyperplanes

1973 ◽  
Vol 25 (2) ◽  
pp. 235-249 ◽  
Author(s):  
Hirotaka FUJIMOTO
Keyword(s):  
Projective Space ◽  
Holomorphic Maps

A Big Picard Theorem for Holomorphic Maps into Complex Projective Space

2009 ◽  
Vol 52 (1) ◽  
pp. 154-160
Author(s):  
Yasheng Ye ◽  
Min Ru
Keyword(s):  
Projective Space ◽  
Complex Manifold ◽  
Complex Projective Space ◽  
Holomorphic Maps ◽  
Analytic Subvariety ◽  
Picard Theorem ◽  
Complex Projective

AbstractWe prove a big Picard type extension theoremfor holomorphic maps f : X–A → M, where X is a complex manifold, A is an analytic subvariety of X, and M is the complement of the union of a set of hyperplanes in ℙn but is not necessarily hyperbolically imbedded in ℙn.

Harmonic maps from surfaces into pseudo-Riemannian spheres and hyperbolic spaces

1983 ◽  
Vol 94 (3) ◽  
pp. 483-494 ◽  
Author(s):  
S. Erdem
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Harmonic Maps ◽  
Hyperbolic Spaces ◽  
Euclidean Sphere ◽  
Holomorphic Maps ◽  
Space Forms ◽  
Indefinite Metrics ◽  
Complex Hyperbolic Spaces ◽  
Complex Projective

In [2, 4, 5, 6, 7] Calabi, Barbosa and Chern showedthat there is a 2:1 correspondence between arbitrary pairs of full isotropic (terminology as in [8]) harmonic maps ±φ:M→S2mfrom a Riemann surface to a Euclidean sphere and full totally isotropic holomorphic maps f:M→2mfrom the surface to complex projective space. In this paper we show, very explicitly, how to construct a similar one-to-one correspondence whenS2mis replaced by some other space forms of positive and negative curvatures with their standard (indefinite) metrics obtained by restricting a standard (indefinite) bilinear form on Euclidean space to the tangent spaces. We get over a difficulty encountered by Barbosa of dealing with the zeros of a certain wedge product by a technique adapted from [8]. The case of complex projective space forms (indefinite complex projective and complex hyperbolic spaces) will be considered in a separate paper. Some further developments in classification theorems are given by Eells and Wood [8], Rawnsley[14], [15] and Erdem and Wood [10].

scholarly journals Embedding Feynman integral (Calabi-Yau) geometries in weighted projective space

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Jacob L. Bourjaily ◽  
Andrew J. McLeod ◽  
Cristian Vergu ◽  
Matthias Volk ◽  
Matt von Hippel ◽  
...  
Keyword(s):  
Projective Space ◽  
Feynman Integral ◽  
Weighted Projective Space

scholarly journals Interpolation by holomorphic maps from the disc to the tetrablock

2021 ◽  
Vol 498 (2) ◽  
pp. 124951
Author(s):  
Hadi O. Alshammari ◽  
Zinaida A. Lykova
Keyword(s):  
Holomorphic Maps

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 ).

Sign in / Sign up

Export Citation Format

Share Document