Jacobian Nullwerte, periods and symmetric equations for hyperelliptic curves

Guàrdia, Jordi

Annales de l'Institut Fourier, Tome 57 (2007) no. 4, pp. 1253-1283.

Nous proposons une solution au problème de Schottky hyperelliptique. Celle-ci est basée sur l’utilisation de matrices jacobiennes de fonctions thêta et de modèles symétriques pour les courbes hyperelliptiques. Ces ingrédients sont intéressants en eux-mêmes  : le premier fournit des matrices de périodes qui peuvent être décrites géométriquement et le second possède de remarquables propriétés arithmétiques.

We propose a solution to the hyperelliptic Schottky problem, based on the use of Jacobian Nullwerte and symmetric models for hyperelliptic curves. Both ingredients are interesting on its own, since the first provide period matrices which can be geometrically described, and the second have remarkable arithmetic properties.

Classification : 11G30, 14H42
Keywords: Hyperelliptic curves, periods, Jacobian Nullwerte
Mot clés : courbes hyperelliptiques, periods, thetanullwerte

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