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Dicritical holomorphic flows on Stein manifolds

Authors:	César Camacho Bruno Scárdua

Institution:	(1) IMPA-Estrada D. Castorina, 110 Jardim Botanico, Rio de Janeiro - RJ, CEP. 22460-320, Brazil;(2) Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21.945-970 Rio de Janeiro-RJ, Brazil;(3) ICTP, Trieste, Italy

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. Bruno Scárdua: Partially supported by ICTP-Trieste-Italy. Received: 27 September 2006

Keywords:	32S65 37F75 32M25
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