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Creators/Authors contains: "Stolovitch, Laurent"

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  1. ; (, Mathematische Annalen)
    Free, publicly-accessible full text available February 1, 2026
  2. ; (, The Journal of Geometric Analysis)
    We construct an injective map from the set of holomorphic equivalence classes of neighborhoods M of a compact complex manifold C into a finite dimension complex Euclidean space when the normal bundle of C in M is fixed and is either weakly negative or 2-positive. 
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  3. ; (, Arnold mathematical journal)
    We consider an embedded n-dimensional compact complex manifold in n+d dimensional complex manifolds. We are interested in the holomorphic classification of neighborhoods as part of Grauert’s formal principle program. We will give conditions ensuring that a neighborhood of C in M is biholomorphic to a neighborhood of the zero section of its normal bundle. This extends Arnold’s result about neighborhoods of a complex torus in a surface. We also prove the existence of a holomorphic foliation in Mn+d having C as a compact leaf, extending Ueda’s theory to the high codimension case. Both problems appear as a kind of linearization problems involving small divisors conditions arising from solutions to their cohomological equations. 
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