论文标题
theta除数和半偶联矢量束的扭转点
Torsion points on theta divisors and semihomogeneous vector bundles
论文作者
论文摘要
根据KEMPF描述$ 2 $ torsion积分的结果，我们将其推广到$ n $ torsion。这是通过Mukai和Oprea引入和研究的某些半偶联矢量束来完成的。作为应用程序，我们证明了theta除数上$ n $ torsion点数的急剧上限，并证明这仅在椭圆曲线的产物中才能实现，并以肯定的猜想构想了Auffarth，Pirola和Salvati Manni。
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 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.
