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June 2003 Infinite-dimensional complex projective varieties
E. Ballico
Bull. Belg. Math. Soc. Simon Stevin 10(2): 263-265 (June 2003). DOI: 10.36045/bbms/1054818027

Abstract

Let $V_i$, $0\le i \le s$, $s \ge 1$, be complex Banach spaces. Assume $V_i$ infinite-dimensional for $1\le i \le s$, $V_0$ finite-dimensional and $V_0 \ne 0$. Let $\pi : {\bf {P}}(V_0)\times \dots \times {\bf {P}}(V_s) \to {\bf {P}}(V_0)$ be the projection. Let $X$ be a closed analytic subset of finite codimension of ${\bf {P}}(V_0)\times \dots \times {\bf {P}}(V_s)$. Here we prove that $\pi (X)$ is a closed analytic subset of ${\bf {P}}(V_0)$ with the following universal property. For every finite-dimensional reduced analytic space $Y$ and every holomorphic map $f: X \to Y$ there is a unique holomorphic map $g: \pi (X) \to Y$ such that $f = g\circ (\pi \vert X)$.

Citation

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E. Ballico. "Infinite-dimensional complex projective varieties." Bull. Belg. Math. Soc. Simon Stevin 10 (2) 263 - 265, June 2003. https://doi.org/10.36045/bbms/1054818027

Information

Published: June 2003
First available in Project Euclid: 5 June 2003

zbMATH: 1052.32016
MathSciNet: MR2015202
Digital Object Identifier: 10.36045/bbms/1054818027

Subjects:
Primary: 14N05, 32K05

Rights: Copyright © 2003 The Belgian Mathematical Society

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Vol.10 • No. 2 • June 2003
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