On reflection maps from the n-space to the n+1-space
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909893596807168 |
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| author | Gama, Milena Barbosa da Silva, Otoniel Nogueira |
| author_facet | Gama, Milena Barbosa da Silva, Otoniel Nogueira |
| contents | In this work we consider some problems about a reflected graph map germ $f$ from $(\mathbb{C}^n,0)$ to $(\mathbb{C}^{n+1},0)$. A reflected graph map is a particular case of a reflection map, which is defined using an embedding of $\mathbb{C}^n$ in $\mathbb{C}^{p}$ and then applying the action of a reflection group $G$ on $\mathbb{C}^{p}$. In this work, we present a description of the presentation matrix of $f_*{\cal O}_n$ as an ${\cal O}_{n+1}$-module via $f$ in terms of the action of the associated reflection group $G$. We also give a description for a defining equation of the image of $f$ in terms of the action of $G$. Finally, we provide an upper (and also a lower) bound for the multiplicity of the image of $f$ and some applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11669 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On reflection maps from the n-space to the n+1-space Gama, Milena Barbosa da Silva, Otoniel Nogueira Algebraic Geometry Complex Variables In this work we consider some problems about a reflected graph map germ $f$ from $(\mathbb{C}^n,0)$ to $(\mathbb{C}^{n+1},0)$. A reflected graph map is a particular case of a reflection map, which is defined using an embedding of $\mathbb{C}^n$ in $\mathbb{C}^{p}$ and then applying the action of a reflection group $G$ on $\mathbb{C}^{p}$. In this work, we present a description of the presentation matrix of $f_*{\cal O}_n$ as an ${\cal O}_{n+1}$-module via $f$ in terms of the action of the associated reflection group $G$. We also give a description for a defining equation of the image of $f$ in terms of the action of $G$. Finally, we provide an upper (and also a lower) bound for the multiplicity of the image of $f$ and some applications. |
| title | On reflection maps from the n-space to the n+1-space |
| topic | Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2408.11669 |