Characterizing gonality for two-component stable curves

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.