A RESIDUE FORMULA FOR MEROMORPHIC CONNECTIONS AND APPLICATIONS TO STABLE SETS OF FOLIATIONS

Masanori Adachi, Séverine Biard, Judith Brinkschulte

correcthigh confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves the cohomological identity c1(L) = -c(Res(∇)) + (i/2π)[Ω] (Proposition 3.3) and then, on a compact Kähler manifold, deduces Ω = 0 and c1(L) = -c(Res(∇)) via Hodge decomposition (Theorem 3.5) . The model independently derives the same identity by comparing a global Chern connection to the given holomorphic connection, applying Stokes on X \ D with tubular boundaries, and identifying the boundary term with the residue divisor; Kähler Hodge decomposition then yields Θ = 0 and c1(L) = -c(Res(∇)). The proofs are methodologically different (total space/zero-section trick vs. direct Stokes on X), but agree in content and conclusions.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The paper presents a clear and correct residue formula for holomorphic connections with holomorphically extendable curvature and shows its Kähler consequences, leading to integrability and localization of the first Chern class. The methods are sound and the applications significant for foliation theory. Minor clarifications (orientation/signs, handling singular loci) would enhance accessibility.