论文标题
亚洲三重的基地宽容阈值和更高的Syzygies
Basepoint-freeness thresholds and higher syzygies on abelian threefolds
论文作者
论文摘要
对于偏光化的阿贝尔（Abelian）品种，Z。Jiang和G. Pareschi引入了一个不变性，并表明如果不变型小，则偏振是无底物或投影正常的。他们的结果被F. caucci推广到更高的Syzygies，即，如果不变型很小，则极化满足属性$（N_P）$。在本文中，我们研究了相对于极化的不变和程度之间的关系。对于阿贝尔三倍，我们使用阿贝尔亚群（Abelian subvarieties）程度给出了不变的上限。特别是，我们肯定地回答了有关作者V. Lozovanu和Caucci在三个维度案例中要求的Abelian品种的一些问题。
For a polarized abelian variety, Z. Jiang and G. Pareschi introduce an invariant and show that the polarization is basepoint free or projectively normal if the invariant is small. Their result is generalized to higher syzygies by F. Caucci, that is, the polarization satisfies property $(N_p)$ if the invariant is small. In this paper, we study a relation between the invariant and degrees of abelian subvarieties with respect to the polarization. For abelian threefolds, we give an upper bound of the invariant using degrees of abelian subvarieties. In particular, we affirmatively answer some questions on abelian varieties asked by the author, V. Lozovanu and Caucci in the three dimensional case.
