Une généralisation d’une construction de Richelot
Author:
Jean-François Mestre
Journal:
J. Algebraic Geom. 22 (2013), 575-580
DOI:
https://doi.org/10.1090/S1056-3911-2012-00589-X
Published electronically:
December 19, 2012
MathSciNet review:
3048546
Full-text PDF
Abstract |
References |
Additional Information
Abstract: We give a generalization of a construction of Richelot, which permits us to obtain a family of dimension $g+1$ of pairs of hyperelliptic curves of genus $g$ with $\overbrace {2\ldots 2}^g$-isogenous Jacobians.
References
- Jean-Benoît Bost and Jean-François Mestre, Moyenne arithmético-géométrique et périodes des courbes de genre $1$ et $2$, Gaz. Math. 38 (1988), 36–64 (French). MR 970659
- F. Richelot, Essai sur une méthode générale pour déterminer la valeur des intégrales ultra-elliptiques, fondée sur des transformations remarquables de ces transcendantes, C.R. Acad. Sci. Paris 2, 1836, 622-627.
- F. Richelot, De transformatione integralium Abelianorum primi ordinis commentatio, J. Reine Angew. Math. $16$, $1837$, 221-341.
- D. Mumford, Tata Lectures on Theta, Birkhauser-Boston, Part II (1983).
- Benjamin Smith, Families of explicit isogenies of hyperelliptic Jacobians, Arithmetic, geometry, cryptography and coding theory 2009, Contemp. Math., vol. 521, Amer. Math. Soc., Providence, RI, 2010, pp. 121–144. MR 2744038, DOI https://doi.org/10.1090/conm/521/10278
References
- J.-B. Bost and J.-F. Mestre, Moyenne arithmético-géometrique et périodes de courbes de genre 1 et 2. Gaz. Math. Soc. France $38$, 1988, 36-64. MR 970659 (89k:14072)
- F. Richelot, Essai sur une méthode générale pour déterminer la valeur des intégrales ultra-elliptiques, fondée sur des transformations remarquables de ces transcendantes, C.R. Acad. Sci. Paris 2, 1836, 622-627.
- F. Richelot, De transformatione integralium Abelianorum primi ordinis commentatio, J. Reine Angew. Math. $16$, $1837$, 221-341.
- D. Mumford, Tata Lectures on Theta, Birkhauser-Boston, Part II (1983).
- B. Smith, Families of Explicit Isogenies of Hyperelliptic Jacobians. In Arithmetic, Geometry, Cryptography and Coding Theory 2009, Contemporary Mathematics 521, Amer. Math. Soc., 2010. MR 2744038
Additional Information
Jean-François Mestre
Affiliation:
Université Paris Diderot, 175 rue du Chevaleret, 75013 Paris, France
Email:
mestre@math.jussieu.fr
Received by editor(s):
October 7, 2010
Received by editor(s) in revised form:
February 2, 2011, and February 9, 2011
Published electronically:
December 19, 2012
