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Log structures, semistable degenerations, log crystalline cohomology, log de Rham cohomology, log smoothness, log Gromov-Witten theory

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When is a map from a logarithmic tangent bundle to a normal bundle surjective?

I guess my answer will be in the category of complex manifolds, therefore we definitely need to assume that $X$ is smooth. I am not that familiar with this language, so I apologize for any stupid mist …
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