Torsion points on theta divisors and semihomogeneous vector bundles

Pareschi, Giuseppe

doi:10.2140/ant.2021.15.1581

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Torsion points on theta divisors and semihomogeneous vector bundles

Giuseppe Pareschi

Vol. 15 (2021), No. 6, 1581–1592

DOI: 10.2140/ant.2021.15.1581

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

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

Vol. 15, No. 6, 2021