Degeneracy theorems for meromorphic mappings of a complete K\"{a}hler manifold sharing hyperplanes in a projective space

Si Duc Quang

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arXiv · 2004.07891

Degeneracy theorems for meromorphic mappings of a complete K\"{a}hler manifold sharing hyperplanes in a projective space

Si Duc Quang

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Abstract

Let $M$ be a complete K\"{a}hler manifold, whose universal covering is biholomorphic to a ball $\mathbb B^m(R_0)$ in $\mathbb C^m$ ($0 C+\rho K)$ hyperplanes in general position regardless of multiplicity with certain positive constants $K$ and $C <2n$ (explicitly estimated), then there are some algebraic relation between them. A degeneracy theorem for $k\ (2\le k\le n+1)$ meromorphic mappings sharing hyperplanes is also given. Our result generalize the previous result in the case where the mappings from $\mathbb C^m$ into $\mathbb P^n(\mathbb C)$.

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Si Duc Quang. 2020-04-14. Degeneracy theorems for meromorphic mappings of a complete K\"{a}hler manifold sharing hyperplanes in a projective space. https://arxiv.org/abs/2004.07891

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