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4 votes
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Morphisms contracting a family of curves

Actually, this is true in more generality: You don't need $f, X$, or $Y$ to be normal or projective (this is of course, trivial, they are all red herrings). You only need $g$ to be proper (I suppose …
Sándor Kovács's user avatar
11 votes
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Generalization of the rigidity lemma in birational geometry

EDIT: I've just realized that this holds under somewhat weaker assumptions. It is not necessary that the fibers of $g$ are connected. EDIT#2: Apparently, in my previous edit I weakened the conditions …
Sándor Kovács's user avatar