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Articles

Uniqueness of holomorphic mappings concerning a question of gross

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Pages 1698-1711 | Received 03 Aug 2020, Accepted 26 Feb 2021, Published online: 14 Mar 2021
 

Abstract

A hypersurface X (resp., a pair of hypersurfaces {Y,Z}) is called a hypersurface (resp., a pair of hypersurfaces) of uniqueness for holomorphic mappings from C to PN(C) if for two non-degenerate holomorphic mappings f,g from C to PN(C), the condition νf(X)=νg(X) (resp., νf(Y)=νg(Y), νf(Z)=νg(Z)) implies fg, where for a mapping φ, νφ(V) denotes the pull-back of a divisor V in PN(C) by φ. In this paper, we give some classes of hypersurfaces and of pairs of hypersurfaces of uniqueness for holomorphic mappings from C to PN(C).

AMS Subject Classifications:

Acknowledgments

The authors are very grateful to the referee for carefully reading the manuscript and for the valuable suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Foundation for Science and Technology Development [grant number 101.02-2018.301].

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