Jets of flat partial connections II

2025/09/16 by Gabriel Fazoli, Fazoli, Gabriel
Mathematics · #32M10 #32M25 #53C12 #53C30 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2509.13510

openalex publication_date 2025/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define and study jets of flat partial connections with respect to singular foliations. In particular, we use the first sheaf of transverse jets to address the problem of extending a flat partial connection to a (flat) meromorphic connection. We then apply our results on the extension problem to classical problems in foliation theory, such as the existence of transversely affine structures and invariant hypersurfaces.

Citations

• Representations of quasiprojective groups, Flat connections and Transversely projective foliations
• Transversely affine foliations on projective manifolds

Related

• Jets of flat partial connections
• Jets of singular foliations
• Good formal structure for meromorphic flat connections on smooth projective surfaces
• Representations of quasiprojective groups, Flat connections and Transversely projective foliations
• On singular foliations tangent to a given hypersurface