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
2015-01-01
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
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
advgeom-2014-0029.pdf
Solo gestori archvio
Tipologia:
Versione Editoriale
Dimensione
417.08 kB
Formato
Adobe PDF
|
417.08 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
|
104451.pdf
accesso aperto
Tipologia:
Post-print
Dimensione
311.92 kB
Formato
Adobe PDF
|
311.92 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
