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arXiv · 2003.09331

Characterizing gonality for two-component stable curves

Juliana Coelho·Frederico Sercio
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Abstract

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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Juliana Coelho, Frederico Sercio. 2020-03-20. Characterizing gonality for two-component stable curves. https://doi.org/10.1007/s10711-021-00609-y

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