Characterizing gonality for two-component stable curves
Tóm tắt
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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