A GEOMETRIC INTERPRETATION OF REDUCTION IN THE JACOBIANS OF Cab CURVES by

نویسندگان

  • Régis Blache
  • Jorge Estrada
  • Maria Petkova
  • MARIA PETKOVA
چکیده

— In this paper, we show that the reduction of divisors in the Jacobian of a curve C can be performed by considering the intersections of a suitable projective model of C with quadrics in projective space. We apply this idea to certain projective model of elliptic and hyperelliptic curves on one hand, and to the canonical model of Cab curves on the other hand, and we find well known algorithms. Résumé (Une interprétation géométrique de la réduction dans la jacobienne des courbes Cab) Dans cet article, nous prouvons que la réduction des diviseurs dans la jacobienne d’une courbe C peut être effectuée en considérant les intersections d’un modèle projectif convenable de C avec des quadriques dans l’espace projectif. Nous appliquons cette idée à certains modèles projectifs des courbes elliptiques et hyperelliptiques d’une part, au modèle canonique des courbes Cab d’autre part, et nous retrouvons des algorithmes bien connus.

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تاریخ انتشار 2010