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.
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.
Keywords: Hyperelliptic curves, periods, Jacobian Nullwerte
Mot clés : courbes hyperelliptiques, periods, thetanullwerte
Guàrdia, Jordi 1
@article{AIF_2007__57_4_1253_0, author = {Gu\`ardia, Jordi}, title = {Jacobian {Nullwerte,} periods and symmetric equations for hyperelliptic curves}, journal = {Annales de l'Institut Fourier}, pages = {1253--1283}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {57}, number = {4}, year = {2007}, doi = {10.5802/aif.2293}, mrnumber = {2339331}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2293/} }
TY - JOUR AU - Guàrdia, Jordi TI - Jacobian Nullwerte, periods and symmetric equations for hyperelliptic curves JO - Annales de l'Institut Fourier PY - 2007 SP - 1253 EP - 1283 VL - 57 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2293/ DO - 10.5802/aif.2293 LA - en ID - AIF_2007__57_4_1253_0 ER -
%0 Journal Article %A Guàrdia, Jordi %T Jacobian Nullwerte, periods and symmetric equations for hyperelliptic curves %J Annales de l'Institut Fourier %D 2007 %P 1253-1283 %V 57 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2293/ %R 10.5802/aif.2293 %G en %F AIF_2007__57_4_1253_0
Guàrdia, Jordi. Jacobian Nullwerte, periods and symmetric equations for hyperelliptic curves. Annales de l'Institut Fourier, Volume 57 (2007) no. 4, pp. 1253-1283. doi : 10.5802/aif.2293. https://aif.centre-mersenne.org/articles/10.5802/aif.2293/
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