A model-theoretic counterpart to Moishezon morphisms

Details A model-theoretic counterpart to Moishezon morphisms A model-theoretic counterpart to Moishezon morphisms

2010-04-27

arxiv.org/abs/1004.4832v1

Mathematics

Logic

12 pages

Scientific paper

In this note a natural strengthening of internality motivated by complex geometry, being "Moishezon" to a set of types, is introduced. Under the hypothesis of Pillay's canonical base property, and using results of Chatzidakis, a criterion is given for when a finite U-rank stationary type that is internal to a nonmodular minimal type is in fact Moishezon to the set of all nonmodular minimal types. This result is a model-theoretic analogue of (a special case of) Campana's "first algebraicity criterion". Other related abstractions from complex geometry, including "coreductions" and "generating fibrations" are also discussed.

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