A remark on Riemann holomorphic extension property (Q1376001)

It is well-known that every holomorphic function on a normal complex space can be holomorphically extended through analytic sets of codimension \(\geq 2\). In general case this result is not true. In this note we investigate the Riemann holomorphic extendability of complex Lie groups. We say that a complex space \(X\) has the Riemann holomorphic extension property in the dimension \(n\) if every holomorphic map from \(Z\setminus S\), where \(Z\) is a normal complex space of dimension \(n\) and \(S\) is an analytic set in \(Z\) of codimension \(\geq 2\), to \(X\) can be holomorphically extended on \(Z\). We prove the following: Theorem. Let \(G\) be a complex Lie group of dimension 2. Then \(G\) has the Riemann holomorphic extension property in the dimension 2 if and only if \(G\) does not contain a compact curve.