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Suppose $A$ is a subvariety of an irreducible complex space(analytic variety) $X$. Is there an analytic hypersurface of $X$ containing $A$?

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    $\begingroup$ If I understand the terminology correctly, no. There are examples of 2-dimensional compact complex manifolds $X$ which contain no compact analytic subvarieties of dimension 1. For such an $X$, take $A$ to be any point in $X$. $\endgroup$
    – Pop
    Commented Dec 17, 2020 at 12:52
  • $\begingroup$ In the algebraic category, this is true. Just take any generator of the ideal of $A$. $\endgroup$
    – Francesco Polizzi
    Commented Dec 17, 2020 at 13:11
  • $\begingroup$ @Pop Thanks. Non-abealian complex torus is in this case. $\endgroup$
    – Ng Chikeung
    Commented Dec 17, 2020 at 16:08
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    $\begingroup$ Also at MSE. $\endgroup$
    – KReiser
    Commented Dec 18, 2020 at 2:48

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