2023/03/07 by Rahim Moosa, Moosa, Rahim · 1 citation
Computer Science · Mathematics · #03C45 #03C60 #32J99 #32M25 #Computer Graphics and Visualization Techniques #FOS: Mathematics #Logic (math.LO) #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2303.04189
openalex publication_date 2023/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.