论文标题
关于丝曲面的Severi问题的注释
A note on the Severi problem for toric surfaces
论文作者
论文摘要
在本说明中，我们迈出了一步，朝分类的曲折表面分类，承认可简化的Severi品种。我们概括了[LAN19，TYO13，TYO14]的结果，并提供了两个感谢您的表面家庭，承认可还原的Severi品种。第一个家庭是一般的，是通过商结构获得的。第二个家庭非常出色，对应于某些狭窄的多边形，我们称之为风筝。我们介绍了两种类型的不变性，它们区分了Severi品种的组件，并允许我们在组件数量上提供下限。在某些情况下，对边界的清晰度进行了验证，并且预计将对足够的线性系统进行一般性。在附录中，我们建立了Severi问题与单变量多项式的拓扑分类之间的联系。
In this note, we make a step towards the classification of toric surfaces admitting reducible Severi varieties. We generalize the results of [Lan19, Tyo13, Tyo14], and provide two families of toric surfaces admitting reducible Severi varieties. The first family is general, and is obtained by a quotient construction. The second family is exceptional, and corresponds to certain narrow polygons, which we call kites. We introduce two types of invariants that distinguish between the components of the Severi varieties, and allow us to provide lower bounds on the numbers of the components. The sharpness of the bounds is verified in some cases, and is expected to hold in general for ample enough linear systems. In the appendix, we establish a connection between the Severi problem and the topological classification of univariate polynomials.
