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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2303.11300 |
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| _version_ | 1866916513483587584 |
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| author | Gryszka, Beata Gwoździewicz, Janusz |
| author_facet | Gryszka, Beata Gwoździewicz, Janusz |
| contents | Let $x=t^n$, $y=\sum_{i=1}^{\infty}a_it^i$ be a parametrisation of the germ of a complex plane analytic curve $Γ$ at the origin. Then $Γ$ has the implicit equation $f(x,y)=0$ in the neighbourhood of the origin, where $f=\sum c_{ij}x^iy^j$ is a Weierstrass polynomial in $\mathbb{C}[[x]][y]$ of degree $n$. Every polynomial depending on coefficients $c_{ij}$ can be expressed as a polynomial depending on the coefficients $a_i$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_11300 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-degeneracy conditions for plane branches Gryszka, Beata Gwoździewicz, Janusz Algebraic Geometry Let $x=t^n$, $y=\sum_{i=1}^{\infty}a_it^i$ be a parametrisation of the germ of a complex plane analytic curve $Γ$ at the origin. Then $Γ$ has the implicit equation $f(x,y)=0$ in the neighbourhood of the origin, where $f=\sum c_{ij}x^iy^j$ is a Weierstrass polynomial in $\mathbb{C}[[x]][y]$ of degree $n$. Every polynomial depending on coefficients $c_{ij}$ can be expressed as a polynomial depending on the coefficients $a_i$. |
| title | Non-degeneracy conditions for plane branches |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2303.11300 |