# Is always a Crepant birational map between smooth varieties a small modification

Lemma: A crepant birational map between quasi-projective normal varieties with only terminal singularities is in fact small modifitacions, i.e. isomorphism in codimension 1.

So, if $f:X\dashrightarrow Y$ is a crepant birational map of smooth varieties and $p\in X$ a point, then $f|_{X-\{p\}} : X-\{ p\} \dashrightarrow Y-\{ f(p)\}$ is a crepant birational map between quasi-projective smooth varieties so is a small modification by the lemma above and then $f$ is a small modification.

Is it right or im missing something?

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I don't see why you're removing a point. As stated, the Lemma applies even before you remove the point. – Hugh Thomas Mar 14 '13 at 18:56
I didnt notice that. So i think that the question is solved. – Joaquín Moraga Mar 15 '13 at 16:23