Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Families of irreducible principally polarized
abelian varieties isomorphic to a product
of elliptic curves

Authors: Víctor González-Aguilera and Rub\'\i{} E. Rodríguez
Journal: Proc. Amer. Math. Soc. 128 (2000), 629-636
MSC (2000): Primary 14K22; Secondary 32G13
Published electronically: October 25, 1999
MathSciNet review: 1676344
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For each $n$ greater than or equal to two, we give a family of
$n$-dimensional, irreducible principally polarized abelian varieties isomorphic to a product of elliptic curves. This family corresponds to the modular curve $X_0(n+1)$.

References [Enhancements On Off] (What's this?)

  • 1. C. H. Clemens and P. A. Griffiths, The intermediate Jacobian of the cubic threefold, Annals of Mathematics 95 (1972), 281-356. MR 46:1796
  • 2. C. J. Earle, H. E. Rauch, Function Theorist, Differential Geometry and Complex Analysis, Chavel, edited by I. Kra and H. M. Farkas, Springer-Verlag, 1985, pp. 15-31. MR 86h:01063
  • 3. C. J. Earle, Some Jacobians which split, Lecture Notes in Mathematics 747, Springer-Verlag, 101-107. MR 80m:14018
  • 4. T. Ekedahl and J.-P. Serre, Exemples de courbes algébriques à jacobienne complètement décomposable, C. R. Acad. Sci. Paris t. 137 Série I (1993), 509-513. MR 94j:14029
  • 5. H. H. Martens, Torelli's Theorem and a generalization for hyperelliptic surfaces, Comm. Pure Appl. Math. 16 (1963), 97-110. MR 27:2623
  • 6. L. Moret-Bailly, Famille de courbes et des variétés abeliennes sur ${\mathbb P}_1$, Asterisque 86 (1981), 109-124.
  • 7. I. Reiner, Automorphisms of the symplectic modular group, Transactions of the A.M.S. 80 (1955), 35-50. MR 17:458a
  • 8. J. F. X. Ries, The splitting of some Jacobi varieties using their automorphism group, Contemp. Math. 201 (1997), 81-124. MR 98c:14022
  • 9. G. Riera and R. E. Rodríguez, The period matrix of Bring's curve, Pacific J. of Math. 154 (1992), 179-200. MR 93e:14033
  • 10. R. E. Rodríguez and V. González-Aguilera, Fermat's quartic curve, Klein's curve and the Tetrahedron, Contemp. Math. 201 (1997), 43-62. MR 97j:14033

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 14K22, 32G13

Retrieve articles in all journals with MSC (2000): 14K22, 32G13

Additional Information

Víctor González-Aguilera
Affiliation: Departamento de Matemáticas, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaíso, Chile

Rub\'\i{} E. Rodríguez
Affiliation: Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago, Chile

Received by editor(s): May 11, 1997
Published electronically: October 25, 1999
Additional Notes: Both authors were supported in part by FONDECYT Grant # 8970007 and Presidential Chair 1997.
Communicated by: Ron Donagi
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society