The Archimedean height pairing for differential forms on degeneration of Riemann surfaces
Differential Geometry
2026-03-06 v1 Algebraic Geometry
Dynamical Systems
Abstract
We define the Archimedean height pairing for fiberwise cohomologically trivial differential forms on a one-parameter degeneration of Riemann surfaces, and we study its asymptotic behavior. The proof relies on recent work by Dai--Yoshikawa on the asymptotics of small eigenvalues. As an application, we relate this pairing to the current-valued pairing of Filip--Tosatti, extending their construction to broader geometric settings.
Keywords
Cite
@article{arxiv.2603.04802,
title = {The Archimedean height pairing for differential forms on degeneration of Riemann surfaces},
author = {Junyu Cao},
journal= {arXiv preprint arXiv:2603.04802},
year = {2026}
}
Comments
45 pages, comments are welcome!