Model-theoretic consequences of a theorem of Campana and Fujiki

• Autorzy: Anand Pillay
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 32J27: Compact K\"ahler manifolds: generalizations, classification
• 03C45: Classification theory, stability and related concepts

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2002
• Tom: 174
• Numer: 2
• Strony: 187-192

Daty

wydano

2002

Twórcy

autor

Anand Pillay

• Department of Mathematics, University of Illinois at Urbana-Champaign, Altgeld Hall, 1409 W. Green St., Urbana, IL 61801, U.S.A.
• Institut für Mathematik, Humboldt Universität, D-10099 Berlin, Germany

Identyfikatory

DOI

10.4064/fm174-2-3