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Let <italic>M</italic> be a complete Kähler manifold, whose universal covering is biholomorphic to a ball 𝔹<italic>m</italic>(<italic>R</italic>0) in ℂ<italic>m</italic> (0 &lt; <italic>R</italic>0 +∞). Our first aim in this paper is to study the algebraic dependence problem of differentiably meromorphic mappings. We will show that if <italic>k</italic> differentibility nonde-generate meromorphic mappings <italic>f</italic>1, …, <italic>fk</italic> of <italic>M</italic> into ℙ<italic>n</italic>(ℂ) (<italic>n</italic> ≥ 2) satisfying the condition (<italic>Cρ</italic>) and sharing few hyperplanes in subgeneral position regardless of multiplicity then <italic>f</italic>1 Λ … Λ <italic>fk</italic>0. For the second aim, we will show that there are at most two different differentiably nondegenerate meromorphic mappings of <italic>M</italic> into ℙ<italic>n</italic>(ℂ) sharing <italic>q</italic> (<italic>q ∼</italic> 2<italic>N − n</italic> + 3 + <italic>O</italic>(<italic>ρ</italic>)) hyperplanes in <italic>N−</italic>subgeneral position regardless of multiplicity. Our results generalize previous finiteness and uniqueness theorems for differentiably meromorphic mappings of ℂ<italic>m</italic> into ℙ<italic>n</italic>(ℂ) and extend some previous results for the case of mappings on Kähler manifold.
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Let M be a complete Kähler manifold, whose universal covering is biholomorphic to a ball 𝔹m(R0) in ℂm (0 < R0 +∞). Our first aim in this paper is to study the algebraic dependence problem of differentiably meromorphic mappings. We will show that if k differentibility nonde-generate meromorphic mappings f1, …, fk of M into ℙn(ℂ) (n ≥ 2) satisfying the condition (Cρ) and sharing few hyperplanes in subgeneral position regardless of multiplicity then f1 Λ … Λ fk0. For the second aim, we will show that there are at most two different differentiably nondegenerate meromorphic mappings of M into ℙn(ℂ) sharing q (q ∼ 2N − n + 3 + O(ρ)) hyperplanes in N−subgeneral position regardless of multiplicity. Our results generalize previous finiteness and uniqueness theorems for differentiably meromorphic mappings of ℂm into ℙn(ℂ) and extend some previous results for the case of mappings on Kähler manifold.

Algebraic dependence and finiteness problems of differentiably nondegenerate meromorphic mappings on Kähler manifolds

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Let M be a complete Kähler manifold, whose universal covering is biholomorphic to a ball 𝔹m(R0) in ℂm (0 < R0 +∞). Our first aim in this paper is to study the...

Algebraic dependence and finiteness problems of differentiably nondegenerate meromorphic mappings on Kähler manifolds

Published Online: Mar 12, 2022

Page range: 271 - 294

Received: Jun 02, 2021

Accepted: Aug 31, 2021

DOI: https://doi.org/10.2478/auom-2022-0015

Keywords
Algebraic dependence, finiteness theorem, Kähler manifold, meromorphic mapping

© 2022 Si Duc Quang, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Algebraic dependence and finiteness problems of differentiably nondegenerate meromorphic mappings on Kähler manifolds

Published Online: Mar 12, 2022

Page range: 271 - 294

Received: Jun 02, 2021

Accepted: Aug 31, 2021

DOI: https://doi.org/10.2478/auom-2022-0015

KeywordsAlgebraic dependence, finiteness theorem, Kähler manifold, meromorphic mapping

© 2022 Si Duc Quang, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Algebraic dependence, finiteness theorem, Kähler manifold, meromorphic mapping