Characterizing gonality for two-component stable curves

Abstract

We study the gonality of curves C over C whose normalization is composed of one or two copies of P 1 . In the first case, C is a nodal curve with g(C) nodes, and we show that gon(C) ≤ g(C)−1 2 if g(C) ≥ 4, with equality holding generically. In the second case, C is a so-called binary curve, and we show that the usual bound gon(C) ≤ g(C)+3 2 holds if g(C) ≥ 2, with equality holding generically.