No CrossRef data available.
Article contents
Discreteness For the Set of Complex Structures On a Real Variety
Published online by Cambridge University Press: 20 November 2018
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
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.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 2003
References
[1]
Bochnak, J. and Huisman, J., When is a complex elliptic curve the product of two real algebraic curves? Math. Ann. 293 (1992), 469–474.Google Scholar
[2]
Brun, J., Sur la simplification dans les isomorphismes analytiques. Ann. Sci. École Norm. Sup. (4) 9 (1976), 533–538.Google Scholar
[3]
Brun, J., Sur la simplification par les variétés homogenes. Math. Ann. 230 (1977), 175–182.Google Scholar
[4]
Fujiki, A., Countability of the Douady space of a complex space. Japan. J. Math. (N.S.) 5 (1979), 431–447.Google Scholar
[5]
Grothendieck, A., Fondements de la géométrie algébrique. extraits du Séminaire Bourbaki 1957–1962.Google Scholar
[6]
Horst, C., Decomposition of compact complex varieties and the cancellation problem. Math. Ann. 271 (1985), 467–477.Google Scholar
[7]
Huisman, J., The underlying real algebraic structure of complex elliptic curves. Math. Ann. 294 (1992), 19–35.Google Scholar
[8]
Parigi, G., Sur la simplification par les tores complexes. J. Reine Angew.Math. 322 (1981), 42–52.Google Scholar
[9]
Parigi, G., Caracterization des variétés compactes simplifiables et applications aux surfaces algébriques. Math. Z. 190 (1985), 371–378.Google Scholar
[10]
Silhol, R., Real Algebraic Surfaces. Lecture Notes in Math. 1392, Springer-Verlag, Berlin, Heidelberg, New York, 1986.Google Scholar
[11]
Weil, A., Adeles and algebraic groups. Progress in Math. 23, Birkhäuser, Boston, Basel, Stuttgart, 1982.Google Scholar
You have
Access