# Holomorphic curves with shift-invariant hyperplane preimages

@article{Halburd2009HolomorphicCW, title={Holomorphic curves with shift-invariant hyperplane preimages}, author={R. G. Halburd and Risto Korhonen and Kazuya Tohge}, journal={Transactions of the American Mathematical Society}, year={2009}, volume={366}, pages={4267-4298} }

If f : C ! P n is a holomorphic curve of hyper-order less than one for which 2n + 1 hyperplanes in general position have forward invariant preimages with respect to the translation �(z) = z +c, then f is periodic with period c 2 C. This result, which can be described as a difference analogue of M. Green's Picard-type theorem for holomorphic curves, follows from a more general result presented in this paper. The proof relies on a new version of Cartan's second main theorem for the Casorati… Expand

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