Model-theoretic consequences of a theorem of Campana and Fujiki

Anand Pillay. "Model-theoretic consequences of a theorem of Campana and Fujiki." Fundamenta Mathematicae 174.2 (2002): 187-192. <http://eudml.org/doc/283304>.

@article{AnandPillay2002,
abstract = {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.},
author = {Anand Pillay},
journal = {Fundamenta Mathematicae},
keywords = {algebraicity; spaces of cycles; compact complex spaces; canonical bases; compact complex manifold; Zilber dichotomy},
language = {eng},
number = {2},
pages = {187-192},
title = {Model-theoretic consequences of a theorem of Campana and Fujiki},
url = {http://eudml.org/doc/283304},
volume = {174},
year = {2002},
}

TY - JOUR
AU - Anand Pillay
TI - Model-theoretic consequences of a theorem of Campana and Fujiki
JO - Fundamenta Mathematicae
PY - 2002
VL - 174
IS - 2
SP - 187
EP - 192
AB - 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.
LA - eng
KW - algebraicity; spaces of cycles; compact complex spaces; canonical bases; compact complex manifold; Zilber dichotomy
UR - http://eudml.org/doc/283304
ER -