Abstract
We survey three constructions of metrized line bundles on the moduli of curves by means of Abel-Jacobi maps, uniformizations, and projective embeddings. We also describe two arithmetic applications: one to the uniform Bogomolov conjecture by Xinyi Yuan and the other to the Northcott property for Gross-Schoen cycles and Ceresa cycles.
| Translated title of the contribution | Calculus on arithmetic moduli of curves |
|---|---|
| Original language | Chinese (Traditional) |
| Pages (from-to) | 2059-2068 |
| Number of pages | 10 |
| Journal | Scientia Sinica Mathematica |
| Volume | 54 |
| Issue number | 12 |
| DOIs | |
| State | Published - 2024 |
All Science Journal Classification (ASJC) codes
- General Mathematics
Keywords
- Arakelov metric
- Poincaré metric
- adelic metric
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