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2021•Complex Variables and Elliptic EquationsRequires access

Uniqueness of holomorphic mappings concerning a question of gross

Hà Huy Khoái, Vu Hoai An, Le Quang Ninh

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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 f≡g, 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).

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What this paper is about

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 f≡g, 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).

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Available 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 f≡g, 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).

Key concepts: Holomorphic function, Hypersurface, Mathematics, Uniqueness, Identity theorem, Degenerate energy levels, Divisor (algebraic geometry), Pure mathematics

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