Abstract
We construct an injective map from the set of holomorphic equivalence classes of neighborhoods M of a compact complex manifold C into \({{\mathbb {C}}}^m\) for some \(m<\infty \) when \((TM)|_C\) is fixed and the normal bundle of C in M is either weakly negative or 2-positive.
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Part of work was carried out when X. G. was supported by CNRS and UCA for a visiting position at UCA.
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Research of X. Gong has been partially supported by a grant from the Simons Foundation (award number: 505027) and NSF grant DMS-2054989. Research of L. Stolovitch has been supported by the French government through the UCAJEDI Investments in future project managed by the National Research Agency (ANR) with the reference number ANR-15-IDEX-01.
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Gong, X., Stolovitch, L. A Structure Theorem for Neighborhoods of Compact Complex Manifolds. J Geom Anal 34, 133 (2024). https://doi.org/10.1007/s12220-024-01582-0
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DOI: https://doi.org/10.1007/s12220-024-01582-0