# 2-torsion points on theta divisors

## TL;DR

This paper establishes a precise upper bound for the number of 2-torsion points on theta divisors, confirming that the maximum is attained only by products of elliptic curves, thus settling a conjecture.

## Contribution

It proves a sharp bound for 2-torsion points on theta divisors and characterizes the cases of equality, confirming a conjecture by Marcucci and Pirola.

## Key findings

- Maximum number of 2-torsion points on theta divisors is achieved only by products of elliptic curves.
- The proven bound is sharp and definitive.
- The conjecture of Marcucci and Pirola is settled affirmatively.

## Abstract

In this note we prove a sharp bound for the number of 2-torsion points on a theta divisor and show that this is achieved only in the case of products of elliptic curves. This settles in the affirmative a conjecture of Marcucci and Pirola.