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On holomorphic $\mathbb{C}^*$-actions

Published 19 Aug 2024 in math.CV | (2408.09625v2)

Abstract: In this paper we study holomorphic actions of the complex multiplicative group on complex manifolds around a singular (fixed) point. We prove linearization results for the germ of action and also for the whole action under some conditions on the manifold. This can be seen as a follow-up to previous works of M. Suzuki and other authors.

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