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We establish a logarithmic Bott localization formula for global holomorphic sections of on a compact complex manifold with simple normal crossings divisor . The zero scheme is allowed to have non-isolated compact components, assumed to be local complete intersections and to satisfy the natural Bott nondegeneracy condition. We further give a current-theoretic formulation and, in the local complete intersection case, identify the local residue term with a Coleff-Herrera current.

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