Weakly regular embeddings of Stein spaces with isolated singularities

Jasna Prezelj

Vol. 220 (2005), No. 1, 141–152

DOI: 10.2140/pjm.2005.220.141

Abstract

We show that any n-dimensional Stein space X with isolated singular points admits a proper holomorphic injective map X → ℂ²ⁿ which is regular on Reg(X). The proof is based on the fact that the Whitney cones C₅(x,X) are at most 2n-dimensional, which means that there exists a neighborhood of x in X having a weakly regular embedding into ℂ²ⁿ. The homotopic principle then enables us to obtain a weakly regular embedding of X into ℂ²ⁿ.

Keywords

Stein space, holomorphic map, weakly regular embedding, homotopic principle, Whitney cone

Mathematical Subject Classification 2000

Primary: 32C15, 32C22, 32E10, 32H02

Milestones

Received: 21 November 2001

Revised: 28 February 2004

Accepted: 9 November 2004

Published: 1 May 2005