Meromorphic degeneration of rational functions over snc models of the projective line
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913683194511360 |
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| author | Irokawa, Reimi |
| author_facet | Irokawa, Reimi |
| contents | For an analytic family $\{f_t\}_{t\in\mathbb{D}^*}$ on the unit punctured disk that meromorphically degenerates at the origin, we show that its limiting measure on an snc model is given by the push forward of the canonical measure attached to the non-archimedean rational function naturally induced from the family, which is a generalization of the results by DeMarco-Faber and Okuyama. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04724 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Meromorphic degeneration of rational functions over snc models of the projective line Irokawa, Reimi Dynamical Systems Algebraic Geometry Complex Variables Primary: 37F10, Secondary: 14G22, 37P30, 32A08 For an analytic family $\{f_t\}_{t\in\mathbb{D}^*}$ on the unit punctured disk that meromorphically degenerates at the origin, we show that its limiting measure on an snc model is given by the push forward of the canonical measure attached to the non-archimedean rational function naturally induced from the family, which is a generalization of the results by DeMarco-Faber and Okuyama. |
| title | Meromorphic degeneration of rational functions over snc models of the projective line |
| topic | Dynamical Systems Algebraic Geometry Complex Variables Primary: 37F10, Secondary: 14G22, 37P30, 32A08 |
| url | https://arxiv.org/abs/2502.04724 |