Is it true that the singular locus of an irreducible hypersurface in $\mathbb{P}^3$ have pure co-dimension ?
$\begingroup$
$\endgroup$
2
-
12$\begingroup$ The singular locus of the quartic surface $XY(X-T)^2+Z^4=0$ is the union of the line $X=T$, $Z=0$ and the point $X=Y=Z=0$. $\endgroup$– abxCommented Nov 1, 2018 at 7:00
-
$\begingroup$ However, the non-normal locus of a hypersurface has pure codimension 1. (You really just need S2 for this). $\endgroup$– Karl SchwedeCommented Nov 1, 2018 at 23:01
Add a comment
|