We give a model-theoretic interpretation of a result by Campana and Fujiki on the algebraicity of certain spaces of cycles on compact complex spaces. The model-theoretic interpretation is in the language of canonical bases, and says that if b,c are tuples in an elementary extension 𝓐* of the structure 𝓐 of compact complex manifolds, and b is the canonical base of tp(c/b), then tp(b/c) is internal to the sort (ℙ¹)*. The Zilber dichotomy in 𝓐* follows immediately (a type of U-rank 1 is locally modular or nonorthogonal to the field ℂ*), as well as the "algebraicity" of any subvariety X of a group G definable in 𝓐* such that Stab(X) is trivial.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm174-2-3,
author = {Anand Pillay},
title = {Model-theoretic consequences of a theorem of Campana and Fujiki},
journal = {Fundamenta Mathematicae},
volume = {173},
year = {2002},
pages = {187-192},
zbl = {1004.03032},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm174-2-3}
}
Anand Pillay. Model-theoretic consequences of a theorem of Campana and Fujiki. Fundamenta Mathematicae, Tome 173 (2002) pp. 187-192. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm174-2-3/