1. CMB 2003 (vol 46 pp. 321)
|Discreteness For the Set of Complex Structures On a Real Variety |
Let $X$, $Y$ be reduced and irreducible compact complex spaces and $S$ the set of all isomorphism classes of reduced and irreducible compact complex spaces $W$ such that $X\times Y \cong X\times W$. Here we prove that $S$ is at most countable. We apply this result to show that for every reduced and irreducible compact complex space $X$ the set $S(X)$ of all complex reduced compact complex spaces $W$ with $X\times X^\sigma \cong W\times W^\sigma$ (where $A^\sigma$ denotes the complex conjugate of any variety $A$) is at most countable.
Categories:32J18, 14J99, 14P99