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Arnol’d’s type theorem on a neighborhood of a cycle of rational curves


Arnol’d showed the uniqueness of the complex analytic structure of a small neighborhood of a non-singular elliptic curve embedded in a non-singular surface whose normal bundle satisfies a Diophantine condition in the Picard variety. We show an analogue of this theorem for a neighborhood of a cycle of rational curves.

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The authorwould like to give heartful thanks to Prof. Tetsuo Ueda whose enormous support and insightful comments were invaluable. He thanks Dr. TakahiroMatsushita and Dr. Yuta Nozaki who gave him many valuable comments on the topological aspects of Levi-flat hypersurfaces which is treated in §5. He is supported by Leading Initiative for Excellent Young Researchers (No. J171000201).

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Correspondence to Takayuki Koike.

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Koike, T. Arnol’d’s type theorem on a neighborhood of a cycle of rational curves. JAMA (2022).

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