Automorphisms of Plane Curves defined from Chebychev polynomials
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917361256235008 |
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| author | Tafazolian, Saeed Top, Jaap |
| author_facet | Tafazolian, Saeed Top, Jaap |
| contents | We investigate the automorphism groups of the algebraic curves \[ \mathcal{C}_d : y^d = φ_d(x), \] where $φ_d(x)$ denotes the Chebyshev polynomial of degree $d$, defined over a field $k$ with $p:=\operatorname{char}(k) \nmid 2d$. We determine the full automorphism group of $\mathcal{C}_d$ in all the cases considered in this paper, namely for $d=4$, and more generally when $2d = p^r+1$ or $4d = p^r+1$. For all other $d>4$, Expectation~\ref{3.19} predicts what the automorphism group should be.
As an application, we show that certain maximal curves of the same genus are not isomorphic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01216 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Automorphisms of Plane Curves defined from Chebychev polynomials Tafazolian, Saeed Top, Jaap Algebraic Geometry We investigate the automorphism groups of the algebraic curves \[ \mathcal{C}_d : y^d = φ_d(x), \] where $φ_d(x)$ denotes the Chebyshev polynomial of degree $d$, defined over a field $k$ with $p:=\operatorname{char}(k) \nmid 2d$. We determine the full automorphism group of $\mathcal{C}_d$ in all the cases considered in this paper, namely for $d=4$, and more generally when $2d = p^r+1$ or $4d = p^r+1$. For all other $d>4$, Expectation~\ref{3.19} predicts what the automorphism group should be. As an application, we show that certain maximal curves of the same genus are not isomorphic. |
| title | Automorphisms of Plane Curves defined from Chebychev polynomials |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2505.01216 |