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Jun 18, 2018 at 10:07 history edited Evgeny Shinder CC BY-SA 4.0
"UPDATE" added
Jun 18, 2018 at 9:53 comment added Jason Starr If the codimension of the singular set is $4$ (rather than $3$, as in your case), the standard reference is SGA 2, specifically Grothendieck's proof of the Samuel Conjecture. However, for codimension $3$, the (Weil divisor) class group can be larger than the Picard group, e.g., this happens if $f(z,w)$ equals $zw$.
Jun 18, 2018 at 9:44 history edited Evgeny Shinder CC BY-SA 4.0
Typo fixed
Jun 18, 2018 at 9:28 history asked Evgeny Shinder CC BY-SA 4.0