On the Saito number of plane curves
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929392098213888 |
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| author | Genzmer, Yohann Hernandes, Marcelo E. |
| author_facet | Genzmer, Yohann Hernandes, Marcelo E. |
| contents | In this work we study the \emph{Saito number} of a plane curve and we present a method to determine the minimal Saito number for plane curves in a given equisingularity class, that gives rise to an actual algorithm. In particular situations, we also provide various formulas for this number. In addition, if $ν_0$ and $ν_1$ are two coprime positive integers and $N>0$ then we show that for any $1\leq k\leq \left [\frac{Nν_0}{2}\right ]$ there exits a plane curve equisingular to the curve $$y^{Nν_0}-x^{Nν_1}=0$$ such that its Saito number is precisely $k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13729 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Saito number of plane curves Genzmer, Yohann Hernandes, Marcelo E. Algebraic Geometry Complex Variables 14H20, 32S65, 14B05 In this work we study the \emph{Saito number} of a plane curve and we present a method to determine the minimal Saito number for plane curves in a given equisingularity class, that gives rise to an actual algorithm. In particular situations, we also provide various formulas for this number. In addition, if $ν_0$ and $ν_1$ are two coprime positive integers and $N>0$ then we show that for any $1\leq k\leq \left [\frac{Nν_0}{2}\right ]$ there exits a plane curve equisingular to the curve $$y^{Nν_0}-x^{Nν_1}=0$$ such that its Saito number is precisely $k$. |
| title | On the Saito number of plane curves |
| topic | Algebraic Geometry Complex Variables 14H20, 32S65, 14B05 |
| url | https://arxiv.org/abs/2406.13729 |