= Irreducible analytic subvariety of a complex manifold
= Irreducible analytic subvariety
{synonym}
An analytic subvariety is a closed subset locally defined by finitely many <holomorphic functions>. It is irreducible if it is not the union of two proper closed analytic subsets. An irreducible analytic subvariety of complex codimension $k$ in an $n$-dimensional <complex manifold> has pure complex dimension $n-k$. Global irreducibility does not forbid multiple local branches at a singular point.
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