Dicritical holomorphic flows on Stein manifolds

Abstract.

We study holomorphic flows on Stein manifolds. We prove that a holomorphic flow with isolated singularities and a dicritical singularity of the form $\sum^{n}_{j=1}\lambda_{j}z_{j}\frac{\partial}{\partial z_{j}}+\ldots, \lambda_{j}\in \mathbb{Q}_{+},\forall j \in \{1,\ldots,n\}$ on a Stein manifold $M^n, n \geq 2$ with ${\mathop{H}\limits^{\vee}}{^{2}}(M^{n}, {{{\mathbb{Z}}}})=0$, is globally analytically linearizable; in particular M is biholomorphic to ${\mathbb{C}}^{n}$. A complete stability result for periodic orbits is also obtained.