Let $(X, \mathcal O_X)$ be an irreducible variety. Say $Y$ is a closed irreducible sub variety. Then is it true that $Y$ is smooth iff the local ring of $Y$ i.e. $\mathcal O_{X,Y}$ is regular ?
2026-03-25 04:39:27.1774413567
Local ring of a smooth subvariety.
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