Fay’s trisecant formula shows that the Kummer variety of the Jacobian of a smooth projectivecurve has a four-dimensional family of trisecant lines. We study when these lines intersect thetheta divisor of the Jacobian and prove that the Gauss map of the theta divisor is constant onthese points of intersection, when defined. We investigate the relation between the Gauss mapand multisecant planes of the Kummer variety as well.
The Gauss map and secants of the Kummer variety / AUFFARTH II, ROBERT FREDERICK; Codogni, Giulio; Salvati Manni, Riccardo. - In: BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6093. - 51:3(2019), pp. 489-500. [10.1112/blms.12244]
The Gauss map and secants of the Kummer variety
Salvati Manni, Riccardo
2019
Abstract
Fay’s trisecant formula shows that the Kummer variety of the Jacobian of a smooth projectivecurve has a four-dimensional family of trisecant lines. We study when these lines intersect thetheta divisor of the Jacobian and prove that the Gauss map of the theta divisor is constant onthese points of intersection, when defined. We investigate the relation between the Gauss mapand multisecant planes of the Kummer variety as well.| File | Dimensione | Formato | |
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