Submission date: 7 March 2023

Abstract:

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 CCM-structure. A first-order axiomatisation of existentially closed differential CCM-structures is given. The resulting theory, DCCM, is a common expansion of the theories of differentially closed fields and compact complex manifolds. A study of the basic model theory of DCCM is initiated, including proofs of completeness, quantifier elimination, elimination of imaginaries, and total transcendentality. The finite-dimensional types in DCCM are shown to be precisely the generic types of meromorphic vector fields.

Mathematics Subject Classification: 03C60, 03C45, 32M25, 32J99

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Full text arXiv 2303.04189: pdf, ps.