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For questions related to divisors in the sense of algebraic geometry (Cartier divisors, Weil divisors and so on). For question on divisors in the number theoretic sense please use the tag divisors-multiples.
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singular $m$-canonical divisors
Let $S\subseteq|mK_X|$ be the set of singular divisors.
Is $S$ always a hypersurface, i.e., without irreducible component of codimension $\geqslant 2$ ? …