It is a well-known result that a stable curve of compact type over \({\mathbb {C}}\) having two components is hyperelliptic if and only if both components are hyperelliptic and the point of intersection is a Weierstrass point for each of them. With the use of admissible covers, we generalize this characterization in two ways: for stable curves of higher gonality having two smooth components and one node; and for hyperelliptic and trigonal stable curves having two smooth non-rational components and any number of nodes.

中文翻译：

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表征两成分稳定曲线的多边形

众所周知的结果是，当且仅当两个分量均为超椭圆且交点为每个的Weierstrass点时，具有两个分量的\（{\ mathbb {C}} \）上的紧凑型稳定曲线为超椭圆形其中。通过使用可允许的覆盖，我们通过两种方式来概括该特征：对于具有两个平滑分量和一个节点的较高多边形的稳定曲线；对于具有两个平滑非有理分量和任意数量节点的超椭圆和三角形稳定曲线。