On the Stein property of the complement to an algebraic hypersurface in a toric variety
type: Item
instance of: scholarly article
title: On the Stein property of the complement to an algebraic hypersurface in a toric variety
zbMATH Open document ID: 0924.32013
DOI: 10.1007/BF02673918
author: O. V. Yakovleva
published in: Siberian Mathematical Journal
publication date: 1999-05-11T00:00:00Z
review text: It was shown by \textit{C. O. Kiselman} [Acta Math. 117, 1-35 (1967; Zbl 0152.07602)] that the complement \({\mathbb P}^n \setminus V\) to an algebraic hypersurface \(V\) in a complex projective space \({\mathbb P}^n\) is a Stein manifold. In the article under consideration, the question is discussed about the Stein property of the complement \(M^n \setminus V\) to an algebraic surface \(V\) in an arbitrary toric variety \(M^n\). It is shown that, given a polynomial function \(F(z)\) of affine coordinates \(z \in {\mathbb C}^n\), it is possible to construct a canonical (native) toric variety \(M^n\), a compactification of the space \({\mathbb C}^n\), for which \(M^n \setminus V\) is a Stein manifold, where \(V\) is the closure of the hypersurface \(\{ z \in \mathbb C^n : F(z) = 0 \}\) in \(M^n\). This result is a generalization of the corresponding result of the author for the case of curves \(V\) in \({\overline{\mathbb C}}^2\).
Mathematics Subject Classification ID: 32E10
Mathematics Subject Classification ID: 14M25
Mathematics Subject Classification ID: 32J05
zbMATH DE Number: 1286462
zbMATH Keywords: Stein property
zbMATH Keywords: toric variety
zbMATH Keywords: Newton polyhedron
MaRDI profile type: Publication
cites work: On entire functions of exponential type and indicators of analytic functionals
cites work: Introduction to Toric Varieties. (AM-131)
cites work: THE GEOMETRY OF TORIC VARIETIES
description: scientific article; zbMATH DE number 1286462