Characterizing gonality for two-component stable curves
arXiv:2003.09331 · doi:10.1007/s10711-021-00609-y
Abstract
It is a well-known result that a stable curve of compact type over 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.
2 figures, commentas are welcome