Strict germs on normal surface singularities
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
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| _version_ | 1866915701133934592 |
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| author | Ruggiero, Matteo |
| author_facet | Ruggiero, Matteo |
| contents | We show that any holomorphic germ $f \colon (X,x_0) \to (Y,y_0)$ of topological degree $1$ between normal surface singularities can be written as $f=π\circ σ$, where $π\colon Y' \to (Y,y_0)$ is a modification and $σ\colon (X,x_0) \to (Y',y_1)$ is a local isomorphism sending $x_0$ to a point $y_1 \in π^{-1}(y_0)$. A result by Fantini, Favre and myself guarantees that when $f$ is a selfmap, then $(X,x_0)$ is a sandwiched singularity. We give here an alternative proof based on the construction of the associated Kato surfaces, and valuative dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24699 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strict germs on normal surface singularities Ruggiero, Matteo Algebraic Geometry Complex Variables 32S45, 32H02, 13A18, 37P50 We show that any holomorphic germ $f \colon (X,x_0) \to (Y,y_0)$ of topological degree $1$ between normal surface singularities can be written as $f=π\circ σ$, where $π\colon Y' \to (Y,y_0)$ is a modification and $σ\colon (X,x_0) \to (Y',y_1)$ is a local isomorphism sending $x_0$ to a point $y_1 \in π^{-1}(y_0)$. A result by Fantini, Favre and myself guarantees that when $f$ is a selfmap, then $(X,x_0)$ is a sandwiched singularity. We give here an alternative proof based on the construction of the associated Kato surfaces, and valuative dynamics. |
| title | Strict germs on normal surface singularities |
| topic | Algebraic Geometry Complex Variables 32S45, 32H02, 13A18, 37P50 |
| url | https://arxiv.org/abs/2512.24699 |