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arXiv · 2603.04802

The Archimedean height pairing for differential forms on degeneration of Riemann surfaces

Junyu Cao
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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.

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Junyu Cao. 2026-03-05. The Archimedean height pairing for differential forms on degeneration of Riemann surfaces. https://arxiv.org/abs/2603.04802

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