论文标题
从分支点恢复平面曲线
Recovery of Plane Curves from Branch Points
论文作者
论文摘要
我们从投影下的分支点恢复了平面曲线。我们的重点在于立方体和四分之一。这些分别具有6和12个分支点。 Hurwitz飞机数40和120计数解决方案的轨道。我们确定实际解决方案的数量，并提出了精确的算法以恢复。我们的方法依赖于150年的美丽代数几何形状，从克莱斯施到瓦基尔及其他地区。
We recover plane curves from their branch points under projection onto a line. Our focus lies on cubics and quartics. These have 6 and 12 branch points respectively. The plane Hurwitz numbers 40 and 120 count the orbits of solutions. We determine the numbers of real solutions, and we present exact algorithms for recovery. Our approach relies on 150 years of beautiful algebraic geometry, from Clebsch to Vakil and beyond.
