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arXiv 2003.093312020-03-20math.AG

两分量稳定曲线的 gonality 刻画

Characterizing gonality for two-component stable curves

Juliana Coelho, Frederico Sercio

备注：: 2 figures, commentas are welcome
DOI：: 10.1007/s10711-021-00609-y

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AI总结：

本文利用可容许覆盖，将两分量稳定曲线的超椭圆刻画推广到更高 gonality 及超椭圆和三叉情形，涵盖任意节点数。

摘要：

众所周知，在复数域 $\mathbb{C}$ 上具有两个分量的紧致型稳定曲线是超椭圆曲线，当且仅当两个分量都是超椭圆曲线，且交点对每个分量都是 Weierstrass 点。利用可容许覆盖，我们将这一刻画以两种方式推广：对于具有两个光滑分量和一个节点的更高 gonality 稳定曲线；以及对于具有两个光滑非有理分量和任意数量节点的超椭圆和三叉稳定曲线。

英文摘要：

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.

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