Characterizing gonality for two-component stable curves

Geometriae Dedicata - Tập 214 - Trang 157-176 - 2021
Juliana Coelho1, Frederico Sercio2
1Instituto de Matemática e Estatística - Rua Prof. Marcos Waldemar de Freitas Reis, Universidade Federal Fluminense (UFF), Niterói, Brasil
2Departamento de Matemática, Rua José Lourenço Kelmer, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, Brasil

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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