Double points and image of reflection maps
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
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| _version_ | 1866916314699792384 |
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| author | Zampiva, Jose Rafael Borges Penafort-Sanchis, Guillermo Orefice-Okamoto, Bruna Tomazella, Joao Nivaldo |
| author_facet | Zampiva, Jose Rafael Borges Penafort-Sanchis, Guillermo Orefice-Okamoto, Bruna Tomazella, Joao Nivaldo |
| contents | A reflection mapping is a singular holomorphic mapping obtained by restricting the quotient mapping of a complex reflection group. We study the analytic structure of double point spaces of reflection mappings. In the case where the image is a hypersurface, we obtain explicit equations for the double point space and for the image as well. In the case of surfaces in $\C^3$, this gives a very efficient method to compute the Milnor number and delta invariant of the double point curve. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_06792 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Double points and image of reflection maps Zampiva, Jose Rafael Borges Penafort-Sanchis, Guillermo Orefice-Okamoto, Bruna Tomazella, Joao Nivaldo Algebraic Geometry 32S25 A reflection mapping is a singular holomorphic mapping obtained by restricting the quotient mapping of a complex reflection group. We study the analytic structure of double point spaces of reflection mappings. In the case where the image is a hypersurface, we obtain explicit equations for the double point space and for the image as well. In the case of surfaces in $\C^3$, this gives a very efficient method to compute the Milnor number and delta invariant of the double point curve. |
| title | Double points and image of reflection maps |
| topic | Algebraic Geometry 32S25 |
| url | https://arxiv.org/abs/2312.06792 |