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Sep 3, 2020 at 22:39 comment added KReiser The ramification locus is just the support of the sheaf $\Omega_{X/Y}$ on $X$. This is in many texts. To get examples with $X,Y$ singular, all you need to do is to compute what $\Omega_{X/Y}$ for a map of singular varieties $X\to Y$ and see where it's supported.
Sep 3, 2020 at 17:19 history asked xin fu CC BY-SA 4.0