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infinite-dimensional complex projective space; infinite-dimensional complex manifold; complete intersection; complex Banach space; complex Banach manifold
Let $V$ be an infinite-dimensional complex Banach space and $X \subset {\mathbf {P}}(V)$ a closed analytic subset with finite codimension. We give a condition on $X$ which implies that $X$ is a complete intersection. We conjecture that the result should be true for more general topological vector spaces.
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