2024/08/26 by Richard Hain, Hain, Richard · 1 citation
Engineering · Mathematics · Physics and Astronomy · #14C30 #Algebraic Geometry (math.AG) #Elasticity and Wave Propagation #FOS: Mathematics #Mathematics and Applications #Scientific Research and Discoveries
paper · pdf · doi:10.48550/arxiv.2408.13997
openalex publication_date 2024/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A real biextension is a real mixed Hodge structure that is an extension of R(0) by a mixed Hodge structure with weights -1 and -2. A unipotent real biextension over an algebraic manifold is a variation of mixed Hodge structure over it, each of whose fibers is a real biextension and whose weight graded quotients are do not vary. We show that if a unipotent real biextension has non abelian monodromy, then its ``general fiber'' does not split. This result is a tool for investigating the boundary behaviour of normal functions and is applied in arXiv:2408.07809 to study the boundary behaviour of the normal function of the Ceresa cycle.