Dimension of holomorphic extensions of complex spaces (Q909067)

Let \(\alpha\) : \(X\to Y\) be a holomorphic map between the complex spaces X and Y; let \({\mathcal O}(X)\), \({\mathcal O}(Y)\) be the global function algebras. (Y,\(\alpha)\) is called holomorphic extension of X if the map \(\alpha^*: {\mathcal O}(Y)\to {\mathcal O}(X)\), \(\alpha^*(f)=f\circ \alpha\), is bijective. The authors investigate the relationship between the dimensions of the spaces X and Y in dependence of holomorphically spreadable holomorphic extension Y of the complex space X. An application is given for normal connected complex spaces.