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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.02693 |
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| _version_ | 1866910186220814336 |
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| author | Campillo, Antonio Delgado, Felix Gusein-Zade, Sabir |
| author_facet | Campillo, Antonio Delgado, Felix Gusein-Zade, Sabir |
| contents | For a subfield $\K$ of the field $\C$ of complex numbers, we consider curve and divisorial valuations on the algebra $\K[[x,y]]$ of formal power series in two variables with the coeficients in $\K$. We compute the semigroup Poincaré series and the classical Poincaré series of a valuation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02693 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Poincaré series of valuations on functions over a field Campillo, Antonio Delgado, Felix Gusein-Zade, Sabir Algebraic Geometry 16W60, 14B05, 14G27 For a subfield $\K$ of the field $\C$ of complex numbers, we consider curve and divisorial valuations on the algebra $\K[[x,y]]$ of formal power series in two variables with the coeficients in $\K$. We compute the semigroup Poincaré series and the classical Poincaré series of a valuation. |
| title | Poincaré series of valuations on functions over a field |
| topic | Algebraic Geometry 16W60, 14B05, 14G27 |
| url | https://arxiv.org/abs/2506.02693 |