A Picard theorem for projective varieties
type: Item
instance of: scholarly article
title: A Picard theorem for projective varieties
zbMATH Open document ID: 0746.32007
author: Peter Hall
published in: Michigan Mathematical Journal
publication date: 1992-06-25T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 32H25
Mathematics Subject Classification ID: 14M25
zbMATH DE Number: 7656
zbMATH Keywords: Picard theorem
zbMATH Keywords: Borel lemma
zbMATH Keywords: toric variety
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029004131
OpenAlex ID: W2062108023
DOI: 10.1307/MMJ/1029004131
description: scientific article; zbMATH DE number 7656