Abstract
The main purpose of this paper is to complete several geometric constructions, developed in [T-V, II] for the study of elliptic solitons associated with a given elliptic curve E. In fact we show that the compactified Jacobian of any tangential cover of degree n over E covers E (n) the nth symmetric product of E. It then follows that the theta divisor of that Jacobian is ample and naturally equipped with a theta function. Last but not least we prove a Torelli theorem for tangential covers within the frame of degree n! coverings of E (n).
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Treibich, A. (1993). Compactified Jacobians of Tangential Covers. In: Babelon, O., Kosmann-Schwarzbach, Y., Cartier, P. (eds) Integrable Systems. Progress in Mathematics, vol 115. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0315-5_2
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DOI: https://doi.org/10.1007/978-1-4612-0315-5_2
Publisher Name: Birkhäuser, Boston, MA
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