Uniqueness problem without multiplicities in value distribution theory
Let \(H_ 1\),..., \(H_ k\) be hyperplanes in general position in \({\mathbb{P}}^ m\) with \(m\geq 2\). Let \(A_ 1\),..., \(A_ k\) be pure (n-1)- dimensional analytic subsets of \({\mathbb{C}}^ n\) with \(co\dim A_ i\cap A_ j\geq 2\) whenever \(i\neq j\). Then any linearly non-degenerate meromorphic maps f,g,h: \({\mathbb{C}}^ n\to {\mathbb{P}}^ m\) with \(f| A_ j=g| A_ j=h| A_ j\) and with \(f^{-1}(H_ j)=G^{-1}(H_ j)=h^{-1}(H_ j)=A_ j\) for \(j=1\),..., k satisfy \(\Pr operty\quad (p)\) if \(k=3m+1\). Consequently, such f, g, h are algebraically dependent. If even \(n\geq rank\) \(f=rank\) \(g=rank\) \(h=\) m, then \(k=m+3\) suffices.
scientific article; zbMATH DE number 4023701