Degeneration of the archimedean height pairing of algebraically trivial cycles
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909976956502016 |
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| author | Chen, Zhelun |
| author_facet | Chen, Zhelun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22788 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Degeneration of the archimedean height pairing of algebraically trivial cycles Chen, Zhelun Algebraic Geometry Number Theory 14G40, 14C30, 14C25 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. |
| title | Degeneration of the archimedean height pairing of algebraically trivial cycles |
| topic | Algebraic Geometry Number Theory 14G40, 14C30, 14C25 |
| url | https://arxiv.org/abs/2512.22788 |