2025/01/25 by Maurício Corrêa, Corrêa, Maurício, Tatsuo Suwa +1
Computer Science · Engineering · #Advanced Malware Detection Techniques #Advancements in Semiconductor Devices and Circuit Design #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Physical Unclonable Functions (PUFs) and Hardware Security #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2501.15133
openalex publication_date 2025/01/25 · openalex created_date 2025/01/29 · openalex updated_date 2026/07/29
We establish the functoriality of Baum--Bott residues under certain conditions. As an application, we show that if F is a holomorphic foliation, of dimension k≤ n/2, on a (possibly non-compact) complex manifold X of dimension \(n\), then its singular set Sing(F) has dimension dim(Sing(F))≥ k-1. This result addresses a longstanding question by Baum and Bott regarding the functoriality of residues. Also, This provides answers to questions posed by Cerveau and Lins Neto concerning foliations of dimension 2 in ℂ4 and Druel regarding holomorphic foliations on projective manifolds. Furthermore, it confirms the Beauville-Bondal conjecture for the maximal degeneracy locus of Poisson structures. Specifically, if X is a (possibly non-compact) complex Poisson manifold with generic rank r ≤ n/2, and the degeneracy locus X ∖ Xr is non-empty, then it contains a component of dimension > r - 2