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Article

Keywords:
infinite-dimensional complex projective space; infinite-dimensional complex manifold; complete intersection; complex Banach space; complex Banach manifold
Summary:
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.
References:
[1] B. Kotzev: Vanishing of the first cohomology group of line bundles on complete intersections in infinite-dimensional projective space. Ph.D. thesis, University of Purdue, 2001.
[2] L. Lempert: The Dolbeaut complex in infinite dimension. J. Amer. Math. Soc. 11 (1998), 485–520. MR 1603858
[3] A. N. Tyurin: Vector bundles of finite rank over infinite varieties. Math. USSR Izvestija 10 (1976), 1187–1204.
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