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.
Pareschi, G. (2021). Torsion points on theta divisors and semihomogeneous vector bundles. ALGEBRA & NUMBER THEORY, 15(6), 1581-1592 [10.2140/ant.2021.15.1581].
Torsion points on theta divisors and semihomogeneous vector bundles
Pareschi Giuseppe
2021-10-01
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.File | Dimensione | Formato | |
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