Motivated by the study of meromorphic vector fields, a model theory
of “compact complex manifolds equipped with a generic derivation”
is here proposed. This is made precise by the notion of a
differential-structure.
A first-order axiomatisation of existentially closed differential
-structures is given.
The resulting theory,
,
is a common expansion of the theories of differentially closed fields
and compact complex manifolds. A study of the basic model theory of
is
initiated, including proofs of completeness, quantifier elimination, elimination of
imaginaries, and total transcendentality. The finite-dimensional types in
are
shown to be precisely the generic types of meromorphic vector fields.
Keywords
compact complex manifolds, meromorphic vector fields,
differentially closed fields, model theory
