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(made the question clearer and added the hypothesis of normality)
IMeasy
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projective map from $\overline{\mathcal{M}}_{0,n}$

Suppose I have a morphism $f:\overline{\mathcal{M}}_{0,n} \to \mathbb{P}^N$ birational onto its image, and I know exactly what $F$-curves are contracted (or "dually", what divisors are contracted). Suppose furthermore that the image is a normal variety. Is this information in some way sufficient to determine what type of singularities will the image have? How do I detect the kind of singularities just by knowing the exceptional curves?

IMeasy
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