Every divisorial contraction to a curve between terminal threefolds is a weighted blow-up, and all such contractions are classified for smooth curves.
Gunning and Hugo Rossi, Analytic functions of several complex variables, AMS Chelsea Publishing, Providence, RI, 2009, Reprint of the 1965 original
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On the divisorial contractions to curves of threefolds
Every divisorial contraction to a curve between terminal threefolds is a weighted blow-up, and all such contractions are classified for smooth curves.