Geodesic
Discreteness For the Set of Complex Structures On a Real Variety
Canadian mathematical bulletin, Tome 46 (2003) no. 3, pp. 321-322

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2003-033-7
Mots-clés : 32J18, 14J99, 14P99 
Ballico, E. Discreteness For the Set of Complex Structures On a Real Variety. Canadian mathematical bulletin, Tome 46 (2003) no. 3, pp. 321-322. doi: 10.4153/CMB-2003-033-7
@article{10_4153_CMB_2003_033_7,
     author = {Ballico, E.},
     title = {Discreteness {For} the {Set} of {Complex} {Structures} {On} a {Real} {Variety}},
     journal = {Canadian mathematical bulletin},
     pages = {321--322},
     year = {2003},
     volume = {46},
     number = {3},
     doi = {10.4153/CMB-2003-033-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-033-7/}
}
TY  - JOUR
AU  - Ballico, E.
TI  - Discreteness For the Set of Complex Structures On a Real Variety
JO  - Canadian mathematical bulletin
PY  - 2003
SP  - 321
EP  - 322
VL  - 46
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-033-7/
DO  - 10.4153/CMB-2003-033-7
ID  - 10_4153_CMB_2003_033_7
ER  - 
%0 Journal Article
%A Ballico, E.
%T Discreteness For the Set of Complex Structures On a Real Variety
%J Canadian mathematical bulletin
%D 2003
%P 321-322
%V 46
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-033-7/
%R 10.4153/CMB-2003-033-7
%F 10_4153_CMB_2003_033_7

[1] [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] [2] Brun, J., Sur la simplification dans les isomorphismes analytiques. Ann. Sci. École Norm. Sup. (4) 9 (1976), 533–538. Google Scholar

[3] [3] Brun, J., Sur la simplification par les variétés homogenes. Math. Ann. 230 (1977), 175–182. Google Scholar

[4] [4] Fujiki, A., Countability of the Douady space of a complex space. Japan. J. Math. (N.S.) 5 (1979), 431–447. Google Scholar

[5] [5] Grothendieck, A., Fondements de la géométrie algébrique. extraits du Séminaire Bourbaki 1957–1962. Google Scholar

[6] [6] Horst, C., Decomposition of compact complex varieties and the cancellation problem. Math. Ann. 271 (1985), 467–477. Google Scholar

[7] [7] Huisman, J., The underlying real algebraic structure of complex elliptic curves. Math. Ann. 294 (1992), 19–35. Google Scholar

[8] [8] Parigi, G., Sur la simplification par les tores complexes. J. Reine Angew.Math. 322 (1981), 42–52. Google Scholar

[9] [9] Parigi, G., Caracterization des variétés compactes simplifiables et applications aux surfaces algébriques. Math. Z. 190 (1985), 371–378. Google Scholar

[10] [10] Silhol, R., Real Algebraic Surfaces. Lecture Notes in Math. 1392, Springer-Verlag, Berlin, Heidelberg, New York, 1986. Google Scholar

[11] [11] Weil, A., Adeles and algebraic groups. Progress in Math. 23, Birkhäuser, Boston, Basel, Stuttgart, 1982. Google Scholar

Cité par Sources :