Infinite-dimensional complex projective spaces and complete intersections

Abstract: Let $V$ be an infinite-dimensional complex Banach space and $X \subset {\bf {P}}(V)$ 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.

Keywords: infinite-dimensional complex projective space, infinite-dimensional complex manifold, complete intersection, complex Banach space, complex Banach manifold

Classification (MSC2000): 32K05

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