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Discreteness For the Set of Complex Structures On a Real Variety

Published online by Cambridge University Press:  20 November 2018

E. Ballico
E. Ballico*
Affiliation:
Department of Mathematics University of Trento 38050 Povo (TN) Italy, e-mail: ballico@science.unitn.it
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Abstract

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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.

Keywords

32J1814J9914P99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 46 , Issue 3 , 01 September 2003 , pp. 321 - 322
Copyright
Copyright © Canadian Mathematical Society 2003

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