论文标题
具有最大屈曲和Zariski对的平面曲线的扭转分隔线
Torsion divisors of plane curves with maximal flexes and Zariski pairs
论文作者
论文摘要
复杂平面曲线的嵌入拓扑与椭圆曲线的（组理论）算术之间存在密切的关系。在最近的一篇论文中，我们研究了曲线的某些布置拓扑结构，包括特殊平滑的组件，这些曲线是通过与其余部分相关的特殊曲线中的除数引起的扭转特性，这是算术特性。当这条特殊曲线具有最大的屈曲时，其雅各布品种与其PICARD组的零部分之间存在天然同构。在本文中，我们考虑包含具有最大屈曲的特殊平滑组件的曲线布置，并利用这些特性获得Zariski元素，这些元素显示了拓扑，几何和算术之间的相互作用。
There is a close relationship between the embedded topology of complex plane curves and the (group-theoretic) arithmetic of elliptic curves. In a recent paper, we studied the topology of some arrangements of curves which include a special smooth component, via the torsion properties induced by the divisors in the special curve associated to the remaining components, which is an arithmetic property. When this special curve has maximal flexes, there is a natural isomorphism between its Jacobian variety and the degree zero part of its Picard group. In this paper we consider curve arrangements which contain a special smooth component with a maximal flex and exploit these properties to obtain Zariski tuples which show the interplay between topology, geometry and arithmetic.
