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

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

Authors