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.

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Keywords
abelian varieties, theta divisors, torsion points
Mathematical Subject Classification
Primary: 14K05, 14K25
Milestones
Received: 23 July 2020
Revised: 2 December 2020
Accepted: 2 January 2021
Published: 16 October 2021
Authors
Giuseppe Pareschi
Dipartimento di Matematica
Università di Roma “Tor Vergata”
Rome
Italy