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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.13455 |
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| _version_ | 1866909261652557824 |
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| author | Campillo, Antonio Delgado, Félix Gusein-Zade, Sabir M. |
| author_facet | Campillo, Antonio Delgado, Félix Gusein-Zade, Sabir M. |
| contents | Earlier, there was computed the Poincaré series of a valuation or of a collection of valuations on the ring of germs of holomorphic functions in two variables. For a collection of several plane curve valuations it appeared to coincide with the Alexander polynomial of the corresponding algebraic link. Recently, the authors defined Poincaré series of a valuation or of a collection of valuations in the real setting. (Actually, there were defined three versions of them, however, one of them was found to be ``not computable''.) These two Poincar'e series were computed for one plane curve valuation. Here we compute them for a plane divisorial valuation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_13455 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Real Poincaré series of a plane divisorial valuation Campillo, Antonio Delgado, Félix Gusein-Zade, Sabir M. Algebraic Geometry 16W60, 14B05 Earlier, there was computed the Poincaré series of a valuation or of a collection of valuations on the ring of germs of holomorphic functions in two variables. For a collection of several plane curve valuations it appeared to coincide with the Alexander polynomial of the corresponding algebraic link. Recently, the authors defined Poincaré series of a valuation or of a collection of valuations in the real setting. (Actually, there were defined three versions of them, however, one of them was found to be ``not computable''.) These two Poincar'e series were computed for one plane curve valuation. Here we compute them for a plane divisorial valuation. |
| title | Real Poincaré series of a plane divisorial valuation |
| topic | Algebraic Geometry 16W60, 14B05 |
| url | https://arxiv.org/abs/2407.13455 |