The Gauss map and secants of the Kummer variety

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.

Minor changes, to appear on the Bulletin of London Mathematical Society

References in corpus (2)

• Cubic threefolds, Fano surfaces and the monodromy of the Gauss map
• The degree of the Gauss map of the theta divisor