Abstract:
Given a pair of commuting holomorphic vector fields defined on a
neighborhood of $(0,0) \in \mathbb{C}^2$, we discuss the problem of
globalizing them as an action of $\mathbb{C}^2$ on a suitable complex surfaces
along with some related questions. A review of Palais' theory about
globalization of local transformation groups is also included in our
discussion.
Key words and phrases:holomorphic local transformation groups, foliations and leaf spaces, holomorphic complete vector fields.
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