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Families of irreducible principally polarized abelian varieties isomorphic to a product of elliptic curves
Author(s):
Víctor
González-Aguilera;
Rub\'\i
E.
Rodríguez
Journal:
Proc. Amer. Math. Soc.
128
(2000),
629-636.
MSC (2000):
Primary 14K22;
Secondary 32G13
Posted:
October 25, 1999
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Abstract:
For each greater than or equal to two, we give a family of -dimensional, irreducible principally polarized abelian varieties isomorphic to a product of elliptic curves. This family corresponds to the modular curve .
References:
- 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
, 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
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Additional Information:
Víctor
González-Aguilera
Affiliation:
Departamento de Matemáticas, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaíso, Chile
Email:
vgonzale@mat.utfsm.cl
Rub\'\i
E.
Rodríguez
Affiliation:
Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago, Chile
Email:
rubi@mat.puc.cl
DOI:
10.1090/S0002-9939-99-05415-5
PII:
S 0002-9939(99)05415-5
Received by editor(s):
May 11, 1997
Posted:
October 25, 1999
Additional Notes:
Both authors were supported in part by FONDECYT Grant # 8970007 and Presidential Chair 1997.
Communicated by:
Ron Donagi
Copyright of article:
Copyright
1999,
American Mathematical Society
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