# The Gauss map and secants of the Kummer variety

## TL;DR

This paper explores the geometric properties of the Kummer variety related to Jacobians of smooth curves, focusing on trisecant lines, the Gauss map, and their intersections with the theta divisor.

## Contribution

It establishes the constancy of the Gauss map on intersection points of trisecant lines with the theta divisor and examines the relation to multisecant planes.

## Key findings

- Gauss map is constant on intersection points with trisecant lines
- Characterization of trisecant lines intersecting the theta divisor
- Relation between multisecant planes and the Gauss map

## 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.