Abstract
v : V y! V 0 between smooth three-dimensional quartics V V4, V 0 V 0 4 in P is a projective isomorphism. This is the original wording of their theorem; in fact, the arguments of [IM] give a much stronger result, namely, they actually prove that smooth quartics are birationally superrigid. The concept of birational rigidity is not visual. Being rather technical, it makes little impression. It is immediate implications of the property of being birationally (super)rigid that are really impressive. For a projective variety X, smooth in codimension 1, and a linear system jDj, free from ®xed components, we de®ne the threshold of canonical adjunction (or, brie y, just threshold) of the pair X;D, setting
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