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Torsion points on theta divisors and semihomogeneous vector bundles
Algebra & Number Theory ( IF 0.9 ) 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.



中文翻译:

θ 除数和半齐次向量丛上的扭点

我们概括为 n- 扭转 Kempf 描述的结果 2- 位于 theta 除数上的扭转点。这是通过 Mukai 和 Oprea 引入和研究的某些半齐次向量丛来实现的。作为一个应用,我们证明了数量的急剧上限n- 扭转点位于 theta 除数上,并表明这仅在椭圆曲线乘积的情况下才能实现,从而肯定了 Auffarth、Pirola 和 Salvati Manni 的猜想。

更新日期:2021-10-17
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