Fp2-maximal curves with many automorphisms are Galois-covered by the Hermitian curve
| Autor: | Fernando Torres, Maria Montanucci, Daniele Bartoli |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Bartoli, D, Montanucci, M & Torres, F 2021, ' F p2-maximal curves with many automorphisms are Galois-covered by the Hermitian curve ', Advances in Geometry, vol. 21, no. 3, pp. 325-336 . https://doi.org/10.1515/advgeom-2021-0013 |
| DOI: | 10.1515/advgeom-2021-0013 |
| Popis: | Let 𝔽 be the finite field of orderq2. It is sometimes attributed to Serre that any curve 𝔽-covered by the Hermitian curveHq+1:yq+1=xq+x${{\mathcal{H}}_{q+1}}:{{y}^{q+1}}={{x }^{q}}+x$is also 𝔽-maximal. For prime numbersqwe show that every 𝔽-maximal curvex$\mathcal{x}$of genusg≥ 2 with | Aut(𝒳) | > 84(g− 1) is Galois-covered byHq+1.${{\mathcal{H}}_{q+1}}.$The hypothesis on | Aut(𝒳) | is sharp, since there exists an 𝔽-maximal curvex$\mathcal{x}$forq= 71 of genusg= 7 with | Aut(𝒳) | = 84(7 − 1) which is not Galois-covered by the Hermitian curveH72.${{\mathcal{H}}_{72}}.$ |
| Databáze: | OpenAIRE |
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