论文标题
seshadri常数在阿贝尔表面
Seshadri constants on abelian surfaces
论文作者
论文摘要
到目前为止，仅在PICARD第一和主要极化的Abelian表面上，Abelian表面上的Seshadri常数才完全理解。除此之外，椭圆曲线的产品还有部分结果。在本文中，我们展示了如何计算任何Abelian表面上任何NEF线束的Seshadri常数。我们仅根据Néron-Severi组开发有效的算法，不仅要计算Seshadri常数，还要计算其Seshadri曲线的数值数据。访问Seshadri曲线使我们能够绘制Seshadri功能并更好地理解其结构。我们表明，在PICARD的第二个情况下，Seshadri函数的复杂性可能在很大程度上变化。我们的结果表明，除了有限的情况外，Seshadri函数的复杂性至少与Cantor函数一样高。
So far, Seshadri constants on abelian surfaces are completely understood only in the cases of Picard number one and on principally polarized abelian surfaces with real multiplication. Beyond that, there are partial results for products of elliptic curves. In this paper, we show how to compute the Seshadri constant of any nef line bundle on any abelian surface over the complex numbers. We develop an effective algorithm depending only on the basis of the Néron-Severi group to compute not only the Seshadri constants but also the numerical data of their Seshadri curves. Access to the Seshadri curves allows us to plot Seshadri functions and better understand their structure. We show that already in the case of Picard number two the complexity of Seshadri functions can vary to a great degree. Our results indicate that aside from finitely many cases the complexity of the Seshadri function is at least as high as in the Cantor function.
