Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Holomorphic maps into complex projective space omitting hyperplanes


Author: Mark L. Green
Journal: Trans. Amer. Math. Soc. 169 (1972), 89-103
MSC: Primary 32A30; Secondary 32H25
MathSciNet review: 0308433
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Using methods akin to those of E. Borel and R. Nevanlinna, a generalization of Picard's theorem to several variables is proved by reduction to a lemma on linear relations among exponentials of entire functions. More specifically, it is shown that a holomorphic map from $ {{\mathbf{C}}^m}$ to $ {{\mathbf{P}}_n}$ omitting $ n + 2$ distinct hyperplanes has image lying in a hyperplane. If the map omits $ n + 2$ or more hyperplanes in general position, the image will lie in a linear subspace of low dimension, being forced to be constant if the map omits $ 2n + 1$ hyperplanes in general position. The limits found for the dimension of the image are shown to be sharp.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 32A30, 32H25

Retrieve articles in all journals with MSC: 32A30, 32H25


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0308433-6
PII: S 0002-9947(1972)0308433-6
Keywords: Picard theorem, value distribution theory, exponential function, Nevanlinna theory, hyperplanes in general position, holomorphic curve, Nevanlinna characteristic function
Article copyright: © Copyright 1972 American Mathematical Society