A Picard theorem for projective varieties
Let \(V\) be an algebraic variety in \(\mathbb{C}\mathbb{P}^ n\) and let \(\Pi_ 0,\ldots,\Pi_ n\) be independent hyperplanes. Let \(f:\mathbb{C}\to V\) be a holomorphic map that omits \(\Pi_ 0,\ldots,\Pi_ n\). Then either \(f(\mathbb{C})\) lies in a proper linear subspace of \(\mathbb{C}\mathbb{P}^ n\) or \(V\) has more than the minimum of contact with \(\Pi_ 0,\ldots,\Pi_ n\). The proof uses the Borel lemma of value-distribution theory to show that the Zariski closure of \(f(\mathbb{C})\) is a (possibly not normal) toric variety.
scientific article; zbMATH DE number 7656