2025/06/18 by Mats Andersson, Andersson, Mats, Richard Lärkäng +1
Mathematics · #Advanced Algebra and Geometry #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2506.15473
openalex publication_date 2025/06/18 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28
Let E→ X be a holomorphic vector bundle. We consider a class of a singular Hermitian metrics on E with analytic singularities that contains all Griffiths negative such metrics. One can define, given a smooth reference metric h0, a current s(E,h,h0) called the associated Segre form, which defines the expected Bott-Chern class and coincides with the usual Segre form of h where it is smooth. We prove that s(E,h,h0) is the limit of the Segre forms of a sequence of smooth metrics if the metric is smooth outside the degeneracy locus, and in general as a limit of Segre forms of metrics with empty degeneracy locus. One can also define an associated Chern form c(E,h,h0). We prove that the Lelong numbers of s(E,h,h0) and c(E,h,h0) are integers if the singularities are integral, and non-negative for s(E,h,h0).