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Mar 5 at 17:44 comment added David Hubbard @abx Apologies! Of course the singular locus is dimension 0 for a normal surface. I'll leave the question up as I would still be interested to know if there is a good way to study the singularities of $\mathcal{X}$ when the special fibre is non-reduced.
Mar 5 at 16:55 comment added abx If $\mathcal{X}$ is normal, its singular locus is finite.
Mar 5 at 16:34 history edited David Hubbard CC BY-SA 4.0
edited body; edited tags
Mar 5 at 15:45 history edited YCor CC BY-SA 4.0
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Mar 5 at 15:15 history asked David Hubbard CC BY-SA 4.0