Abstract

Let $X_1$ and $X_2$ be two compact strongly pseudoconvex CR manifolds of dimension $2n-1\ge 5$ which are boundaries of complex varieties $V_1$ and $V_2$ with only isolated normal singularities in ${ℂ}^{N_1}$ and ${ℂ}^{N_2}$, respectively. We show that any nonconstant CR morphism from $X_1$ to $X_2$ can be extended to a finite holomorphic covering map from $V_1$ to $V_2$ in the case where $V_2$ has only isolated complete intersection singularities. In particular, there is no nonconstant CR morphism between the links of two isolated complete intersection singularities with different embedding codimensions. Finally, using Kohn–Rossi cohomology, we obtain some sufficient conditions for the nonexistence of CR morphisms from $X_1$ to $X_2$.

Keywords

Mathematical Subject Classification

Milestones

Authors