Families of irreducible principally polarized abelian varieties isomorphic to a product of elliptic curves
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- by Víctor González-Aguilera and Rubí E. Rodríguez PDF
- Proc. Amer. Math. Soc. 128 (2000), 629-636 Request permission
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
- C. Herbert Clemens and Phillip A. Griffiths, The intermediate Jacobian of the cubic threefold, Ann. of Math. (2) 95 (1972), 281–356. MR 302652, DOI 10.2307/1970801
- Clifford J. Earle, H. E. Rauch, function theorist, Differential geometry and complex analysis, Springer, Berlin, 1985, pp. 15–31. MR 780033
- Clifford J. Earle, Some Jacobian varieties which split, Complex analysis Joensuu 1978 (Proc. Colloq., Univ. Joensuu, Joensuu, 1978) Lecture Notes in Math., vol. 747, Springer, Berlin, 1979, pp. 101–107. MR 553033
- Torsten Ekedahl and Jean-Pierre Serre, Exemples de courbes algébriques à jacobienne complètement décomposable, C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), no. 5, 509–513 (French, with English and French summaries). MR 1239039
- Henrik H. Martens, Torelli’s theorem and a generalization for hyper-elliptic surfaces, Comm. Pure Appl. Math. 16 (1963), 97–110. MR 152648, DOI 10.1002/cpa.3160160202
- L. Moret-Bailly, Famille de courbes et des variétés abeliennes sur ${\mathbb P}_1$, Asterisque 86 (1981), 109–124.
- Saunders MacLane, Steinitz field towers for modular fields, Trans. Amer. Math. Soc. 46 (1939), 23–45. MR 17, DOI 10.1090/S0002-9947-1939-0000017-3
- John F. X. Ries, The splitting of some Jacobi varieties using their automorphism groups, Extremal Riemann surfaces (San Francisco, CA, 1995) Contemp. Math., vol. 201, Amer. Math. Soc., Providence, RI, 1997, pp. 81–124. MR 1429196, DOI 10.1090/conm/201/02615
- Gonzalo Riera and Rubí E. Rodríguez, The period matrix of Bring’s curve, Pacific J. Math. 154 (1992), no. 1, 179–200. MR 1154738
- Rubí E. Rodríguez and Víctor González-Aguilera, Fermat’s quartic curve, Klein’s curve and the tetrahedron, Extremal Riemann surfaces (San Francisco, CA, 1995) Contemp. Math., vol. 201, Amer. Math. Soc., Providence, RI, 1997, pp. 43–62. MR 1429194, DOI 10.1090/conm/201/02634
Additional Information
- Víctor González-Aguilera
- Affiliation: Departamento de Matemáticas, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaíso, Chile
- Email: vgonzale@mat.utfsm.cl
- Rubí E. Rodríguez
- Affiliation: Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago, Chile
- Email: rubi@mat.puc.cl
- 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
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 629-636
- MSC (2000): Primary 14K22; Secondary 32G13
- DOI: https://doi.org/10.1090/S0002-9939-99-05415-5
- MathSciNet review: 1676344