Weber’s formula for the bitangents of a smooth plane quartic
Alessio Fiorentino
Publications Mathématiques de Besançon no. 2  (2019), p. 5-17

In a section of his 1876 treatise Theorie der Abel’schen Functionen vom Geschlecht 3 Weber proved a formula that expresses the bitangents of a non-singular plane quartic in terms of Riemann theta constants (Thetanullwerte). The present note is devoted to a modern presentation of Weber’s formula. In the end a connection with the universal bitangent matrix is also displayed.

Dans une section de son traité Theorie der Abel’schen Functionen vom Geschlecht 3, paru en 1876, Weber a démontré une formule qui permet de déterminer les équations des bitangentes d’une quartique plane non singulière à partir des constantes theta de Riemann (Thetanullwerte). Le but de cette note est de présenter la formule de Weber en langage moderne. On aussi montre une connexion avec la matrice universelle des bitangentes.

Received : 2018-04-24
Published online : 2019-12-06
DOI : https://doi.org/10.5802/pmb.33
Classification:  14H42,  14H45,  14K25
Keywords: Plane quartics, theta functions, bitangents.
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     author = {Alessio Fiorentino},
     title = {Weber's formula for the bitangents of a smooth plane quartic},
     journal = {Publications Math\'ematiques de Besan\c con},
     publisher = {Presses universitaires de Franche-Comt\'e},
     number = {2},
     year = {2019},
     pages = {5-17},
     doi = {10.5802/pmb.33},
     language = {en},
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Fiorentino, Alessio. Weber’s formula for the bitangents of a smooth plane quartic. Publications Mathématiques de Besançon, no. 2 (2019), pp. 5-17. doi : 10.5802/pmb.33. pmb.centre-mersenne.org/item/PMB_2019___2_5_0/

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