E. Ballico

Analytic Subsets of Products of Infinite-Dimensional
Projective Spaces

Let $V_i$, $1\le i \le s$, be complex topological vector spaces with $V_1$ infinite-dimensional and
$Y$ a closed analytic subset of finite codimension of ${\bf {P}}(V_1)\times \dots \times {\bf {P}}(V_s)$. Here we show that $Y$ is algebraic (at least if each $V_i$ is a Banach space) and that any two points of $Y$ may be connected by a chain of $s+3$ lines contained in $Y$.