#### Vol. 15, No. 6, 2021

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Torsion points on theta divisors and semihomogeneous vector bundles

### Giuseppe Pareschi

Vol. 15 (2021), No. 6, 1581–1592
##### 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 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.

##### Keywords
abelian varieties, theta divisors, torsion points
##### Mathematical Subject Classification
Primary: 14K05, 14K25