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Given a birational contraction morphism $X\rightarrow Y$ of complex normal algebraic varieties. If $Y$ is a smooth variety, what kind of singularities can appear on $X$?

I would be grateful of any reference that point to this question. Im principally interested in know if the singularities of $X$ can be log-terminal.

In the case that im studying $X$ is toroidal so i have only to prove that $X$ is $\mathbb{Q}$-Gorenstein. If $X$ projective then it follows easy. It is true in general?

Thanks in advance.

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    $\begingroup$ Could you define what you call a birational contraction? $\endgroup$
    – abx
    Commented May 8, 2014 at 5:11
  • $\begingroup$ Since $Y$ is smooth it seems to me that if $X\rightarrow Y$ is divisorial then it should be a weighted blow-up. $\endgroup$
    – Puzzled
    Commented May 8, 2014 at 9:14
  • $\begingroup$ A proper morphism $f\colon X \rightarrow Y$, with a divisor $E$ of $X$, such that $dim(f(E))<dim(E)$ and $X-E\rightarrow Y-f(E)$ is an isomorphism. $\endgroup$
    – Joaquín Moraga
    Commented May 16, 2014 at 2:50

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