Torsion points on theta divisors

Abstract

Using the irreducibility of a natural irreducible representation of the theta group of an ample line bundle on an abelian variety, we derive a bound for the number of $n$-torsion points that lie on a given theta divisor. We present also two alternate approaches to attacking the case $n=2$.

The second and fourth authors discovered that one of the methods of the main paper, along with a result of George Kempf, actually gives an optimal bound for the number of 2-torsion points on a theta divisor. This result is added as an appendix to the main paper