We show that the toroidal Lie group G = C^2/L, where L is the lattice generated by (1, 0), (0, 1) and (t, s), with t not in R, is isomorphic to the generalized Jacobian J_L of the complex elliptic curve E with modulus (1, t), defined by any divisor class D ≡ (M) + (N) of E ful lling M − N = [℘(s) : ℘'(s) : 1] in E. This follows from an apparently new relation between the Weierstrass sigma and elliptic function

DI BARTOLO, A., & FALCONE, G. (2015). The periods of the generalized Jacobian of a complex elliptic curve. ADVANCES IN GEOMETRY, 15(1), 127-131 [10.1515/advgeom-2014-0029].

The periods of the generalized Jacobian of a complex elliptic curve

DI BARTOLO, Alfonso
;
FALCONE, Giovanni
2015

Abstract

We show that the toroidal Lie group G = C^2/L, where L is the lattice generated by (1, 0), (0, 1) and (t, s), with t not in R, is isomorphic to the generalized Jacobian J_L of the complex elliptic curve E with modulus (1, t), defined by any divisor class D ≡ (M) + (N) of E ful lling M − N = [℘(s) : ℘'(s) : 1] in E. This follows from an apparently new relation between the Weierstrass sigma and elliptic function
Settore MAT/03 - Geometria
DI BARTOLO, A., & FALCONE, G. (2015). The periods of the generalized Jacobian of a complex elliptic curve. ADVANCES IN GEOMETRY, 15(1), 127-131 [10.1515/advgeom-2014-0029].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/104451
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