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Dicritical holomorphic flows on Stein manifolds

Profile image of Bruno AzevedoBruno Azevedo

2007, Archiv Der Mathematik

https://doi.org/10.1007/S00013-007-2170-Y
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11 pages

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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.

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  19. Bruno Scárdua, Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21.945-970 Rio de Janeiro-RJ, BRAZIL and ICTP, Trieste, Italy e-mail: scardua@impa.br Received: 27 September 2006

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