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Sep 23, 2020 at 16:07 comment added Watson (At least is it true that the Picard number of $\tilde{X}$ is equal to the Picard number of $X$ plus the number of irreducible components of the exceptional divisor $E$ above $p$ ?)
Sep 23, 2020 at 16:03 comment added Watson Dear F_L, in the example of canonical singularities you gave, we observe that the rank of $\mathrm{Pic}(\widetilde{X}/X)$ coincides with the number of irreducible components of $E$. Is that always the case (regardless the type of singularities of $X$) ?
Nov 5, 2014 at 1:27 history edited Puzzled CC BY-SA 3.0
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May 5, 2014 at 14:08 vote accept user49956
Apr 24, 2014 at 17:51 history answered Puzzled CC BY-SA 3.0