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Green's Forms and Meromorphic Functions on Compact Analytic Varieties

Published online by Cambridge University Press:  20 November 2018

Kunihiko Kodaira
Kunihiko Kodaira*
Affiliation:
Institute for Advanced Study, PrincetonN.J.
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Let be a compact complex analytic variety of the complex dimension n with a positive definite Kâhlerian metric [4] ; the local analytic coordinates on will be denoted by z = (z1z2, … , zn). Now, suppose a meromorphic function f(z) defined on as given. Then the poles and zero-points of f(z) constitute an analytic surface in consisting of a finite number of irreducible closed analytic surfaces Γ1, Γ2, … , Γk, each of which is a polar or a zero-point variety of f(z).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 3 , 1951 , pp. 108 - 128
Copyright
Copyright © Canadian Mathematical Society 1951

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