2025/12/28 by Zhelun Chen, Chen, Zhelun
Mathematics · #14C25 #14C30 #14G40 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2512.22788
openalex publication_date 2025/12/28 · openalex created_date 2025/12/31 · openalex updated_date 2026/07/28
We consider the limiting behaviour of the archimedean height pairing for homologically trivial algebraic cycles in a degenerating one-parameter family of smooth projective complex varieties. We conjecture that the limit is controlled by the non-archimedean geometric height pairing of the cycles on the generic fiber and verify this for algebraically trivial cycles, assuming a conjecture of Griffiths on incidence equivalence. Our work offers a more geometric understanding of a related asymptotic result of Brosnan--Pearlstein and suggests a new perspective on the positivity of the Beilinson--Bloch height pairing over a one-variable complex function field.