A special divisor on a double covering of a compact Riemann surface
Let \(C\) denote a nonsingular, projective complex curve. If \(D\) is a divisor on \(C\), let \(c(D)=\deg D - 2 l(D) +2\) denote the Clifford index of \(D\). The author shows two results: (1) If \(C\) admits a special divisor with small Clifford index, then \(C\) is a two-sheeted cover of a curve with genus at most \(c(D)/2\), and (2) conversely, if \(C\) is a two-sheeted cover of a curve of genus \(g'\), then \(C\) has a special divisor \(D\) with \(c(D)=2g'\). The first result is very similar to a theorem proved by \textit{M. Coppens} and \textit{G. Martens} [Compos. Math. 78, No. 2, 193-212 (1991; Zbl 0741.14035)], while the second result is very similar to a theorem proved by \textit{F. Torres} [Manuscr. Math. 83, No. 1, 39-58 (1994; Zbl 0838.14025)].
scientific article; zbMATH DE number 1217278