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Torsion points on theta divisors and semihomogeneous vector bundles
Algebra & Number Theory  (IF0.938),  Pub Date : 2021-10-16, DOI: 10.2140/ant.2021.15.1581
Giuseppe Pareschi

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 lying 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.