Torsion points on theta divisors and semihomogeneous vector bundles

Abstract

We generalize to $n$-torsion a result of Kempf's describing $2$-torsion points lying on a theta divisor. This is accomplished by means of certain semihomogeneous vector bundles introduced and studied by Mukai and Oprea. As an application, we prove a sharp upper bound for the number of $n$-torsion points on a theta divisor, and show that this is achieved only in the case of products of elliptic curves, settling in the affirmative a conjecture of Auffarth, Pirola and Salvati Manni.

Title slightly changed. Published version

References in corpus (1)

• 2-torsion points on theta divisors