Fay's trisecant formula shows that the Kummer variety of the Jacobian of a smooth projective curve has a four-dimensional family of trisecant lines. We study when these lines intersect the theta divisor of the Jacobian and prove that the Gauss map of the theta divisor is constant on these points of intersection, when defined. We investigate the relation between the Gauss map and multisecant planes of the Kummer variety as well.
Auffarth, R., Codogni, G., Salvati Manni, R. (2019). The Gauss map and secants of the Kummer variety. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 51(3), 489-500 [10.1112/blms.12244].
The Gauss map and secants of the Kummer variety
Codogni G.;
2019-01-01
Abstract
Fay's trisecant formula shows that the Kummer variety of the Jacobian of a smooth projective curve has a four-dimensional family of trisecant lines. We study when these lines intersect the theta divisor of the Jacobian and prove that the Gauss map of the theta divisor is constant on these points of intersection, when defined. We investigate the relation between the Gauss map and multisecant planes of the Kummer variety as well.File in questo prodotto:
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