The Gauss map and secants of the Kummer variety. Issue 3 (19th March 2019)

• Record Type: Journal Article
• Authors: Auffarth, Robert; Codogni, Giulio; Salvati Manni, Riccardo
• Is Part Of: Bulletin of the London Mathematical Society. Volume 51:Issue 3(2019)
• Page Start: 489
• Page End: 500
• Publication Date: 2019-03-19
• Subjects: 14H40 -- 14H42 (primary) -- 14K25 (secondary); Mathematics -- Periodicals; 510
• DOI: 10.1112/blms.12244
• Languages: English
• ISSNs: 0024-6093

Abstract

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.